Generalizations Of Thomaes Formula For Zn Curves

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Generalizations of Thomae's Formula for Zn Curves

Author : Hershel M. Farkas
Publisher : Springer Science & Business Media
ISBN 13 : 144197847X
Total Pages : 368 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Generalizations of Thomae's Formula for Zn Curves by : Hershel M. Farkas

Download or read book Generalizations of Thomae's Formula for Zn Curves written by Hershel M. Farkas and published by Springer Science & Business Media. This book was released on 2010-11-10 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Previous publications on the generalization of the Thomae formulae to Zn curves have emphasized the theory's implications in mathematical physics and depended heavily on applied mathematical techniques. This book redevelops these previous results demonstrating how they can be derived directly from the basic properties of theta functions as functions on compact Riemann surfaces. "Generalizations of Thomae's Formula for Zn Curves" includes several refocused proofs developed in a generalized context that is more accessible to researchers in related mathematical fields such as algebraic geometry, complex analysis, and number theory. This book is intended for mathematicians with an interest in complex analysis, algebraic geometry or number theory as well as physicists studying conformal field theory.

Advances on Superelliptic Curves and Their Applications

Author : L. Beshaj
Publisher : IOS Press
ISBN 13 : 1614995206
Total Pages : 387 pages
Book Rating : 4.6/5 (149 download)

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Book Synopsis Advances on Superelliptic Curves and Their Applications by : L. Beshaj

Download or read book Advances on Superelliptic Curves and Their Applications written by L. Beshaj and published by IOS Press. This book was released on 2015-07-16 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book had its origins in the NATO Advanced Study Institute (ASI) held in Ohrid, Macedonia, in 2014. The focus of this ASI was the arithmetic of superelliptic curves and their application in different scientific areas, including whether all the applications of hyperelliptic curves, such as cryptography, mathematical physics, quantum computation and diophantine geometry, can be carried over to the superelliptic curves. Additional papers have been added which provide some background for readers who were not at the conference, with the intention of making the book logically more complete and easier to read, but familiarity with the basic facts of algebraic geometry, commutative algebra and number theory are assumed. The book is divided into three sections. The first part deals with superelliptic curves with regard to complex numbers, the automorphisms group and the corresponding Hurwitz loci. The second part of the book focuses on the arithmetic of the subject, while the third addresses some of the applications of superelliptic curves.

Partitions, q-Series, and Modular Forms

Author : Krishnaswami Alladi
Publisher : Springer Science & Business Media
ISBN 13 : 1461400287
Total Pages : 233 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Partitions, q-Series, and Modular Forms by : Krishnaswami Alladi

Download or read book Partitions, q-Series, and Modular Forms written by Krishnaswami Alladi and published by Springer Science & Business Media. This book was released on 2011-11-01 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partitions, q-Series, and Modular Forms contains a collection of research and survey papers that grew out of a Conference on Partitions, q-Series and Modular Forms at the University of Florida, Gainesville in March 2008. It will be of interest to researchers and graduate students that would like to learn of recent developments in the theory of q-series and modular and how it relates to number theory, combinatorics and special functions.

Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry

Author : Sergey Novikov
Publisher : American Mathematical Soc.
ISBN 13 : 1470455927
Total Pages : 480 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry by : Sergey Novikov

Download or read book Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry written by Sergey Novikov and published by American Mathematical Soc.. This book was released on 2021-04-12 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.

Ramanujan 125

Author : Ae Ja Yee,
Publisher : American Mathematical Soc.
ISBN 13 : 1470410788
Total Pages : 186 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Ramanujan 125 by : Ae Ja Yee,

Download or read book Ramanujan 125 written by Ae Ja Yee, and published by American Mathematical Soc.. This book was released on 2014-10-14 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of an international conference to commemorate the 125th anniversary of Ramanujan's birth, held from November 5-7, 2012, at the University of Florida, Gainesville, Florida. Srinivasa Ramanujan was India's most famous mathematician. This volume contains research and survey papers describing recent and current developments in the areas of mathematics influenced by Ramanujan. The topics covered include modular forms, mock theta functions and harmonic Maass forms, continued fractions, partition inequalities, -series, representations of affine Lie algebras and partition identities, highly composite numbers, analytic number theory and quadratic forms.

The Beltrami Equation

Author : Vladimir Gutlyanskii
Publisher : Springer Science & Business Media
ISBN 13 : 1461431913
Total Pages : 309 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis The Beltrami Equation by : Vladimir Gutlyanskii

Download or read book The Beltrami Equation written by Vladimir Gutlyanskii and published by Springer Science & Business Media. This book was released on 2012-04-23 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the Beltrami equations that play a significant role in Geometry, Analysis and Physics and, in particular, in the study of quasiconformal mappings and their generalizations, Riemann surfaces, Kleinian groups, Teichmuller spaces, Clifford analysis, meromorphic functions, low dimensional topology, holomorphic motions, complex dynamics, potential theory, electrostatics, magnetostatics, hydrodynamics and magneto-hydrodynamics. The purpose of this book is to present the recent developments in the theory of Beltrami equations; especially those concerning degenerate and alternating Beltrami equations. The authors study a wide circle of problems like convergence, existence, uniqueness, representation, removal of singularities, local distortion estimates and boundary behavior of solutions to the Beltrami equations. The monograph contains a number of new types of criteria in the given problems, particularly new integral conditions for the existence of regular solutions to the Beltrami equations that turned out to be not only sufficient but also necessary. The most important feature of this book concerns the unified geometric approach based on the modulus method that is effectively applied to solving the mentioned problems. Moreover, it is characteristic for the book application of many new concepts as strong ring solutions, tangent dilatations, weakly flat and strongly accessible boundaries, functions of finite mean oscillations and new integral conditions that make possible to realize a more deep and refined analysis of problems related to the Beltrami equations. Mastering and using these new tools also gives essential advantages for the reader in the research of modern problems in many other domains. Every mathematics graduate library should have a copy of this book.

Integrable Systems and Algebraic Geometry

Author : Ron Donagi
Publisher : Cambridge University Press
ISBN 13 : 110871577X
Total Pages : 537 pages
Book Rating : 4.1/5 (87 download)

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Book Synopsis Integrable Systems and Algebraic Geometry by : Ron Donagi

Download or read book Integrable Systems and Algebraic Geometry written by Ron Donagi and published by Cambridge University Press. This book was released on 2020-03-02 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

Integrable Systems and Algebraic Geometry: Volume 2

Author : Ron Donagi
Publisher : Cambridge University Press
ISBN 13 : 1108805337
Total Pages : 537 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Integrable Systems and Algebraic Geometry: Volume 2 by : Ron Donagi

Download or read book Integrable Systems and Algebraic Geometry: Volume 2 written by Ron Donagi and published by Cambridge University Press. This book was released on 2020-04-02 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. The articles in this second volume discuss areas related to algebraic geometry, emphasizing the connections of this central subject to integrable systems, arithmetic geometry, Riemann surfaces, coding theory and lattice theory.

Arithmetic, Geometry, Cryptography and Coding Theory

Author : Alp Bassa
Publisher : American Mathematical Soc.
ISBN 13 : 1470428105
Total Pages : 210 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Arithmetic, Geometry, Cryptography and Coding Theory by : Alp Bassa

Download or read book Arithmetic, Geometry, Cryptography and Coding Theory written by Alp Bassa and published by American Mathematical Soc.. This book was released on 2017-03-27 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 15th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT), held at the Centre International de Rencontres Mathématiques in Marseille, France, from May 18–22, 2015. Since the first meeting almost 30 years ago, the biennial AGCT meetings have been one of the main events bringing together researchers interested in explicit aspects of arithmetic geometry and applications to coding theory and cryptography. This volume contains original research articles reflecting recent developments in the field.

Geometry of Riemann Surfaces

Author : William J. Harvey
Publisher : Cambridge University Press
ISBN 13 : 0521733073
Total Pages : 416 pages
Book Rating : 4.5/5 (217 download)

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Book Synopsis Geometry of Riemann Surfaces by : William J. Harvey

Download or read book Geometry of Riemann Surfaces written by William J. Harvey and published by Cambridge University Press. This book was released on 2010-02-11 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Original research and expert surveys on Riemann surfaces.

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 804 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Theory of Generalized Donaldson-Thomas Invariants

Author : Dominic D. Joyce
Publisher : American Mathematical Soc.
ISBN 13 : 0821852795
Total Pages : 212 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Theory of Generalized Donaldson-Thomas Invariants by : Dominic D. Joyce

Download or read book A Theory of Generalized Donaldson-Thomas Invariants written by Dominic D. Joyce and published by American Mathematical Soc.. This book was released on 2011 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies generalized Donaldson-Thomas invariants $\bar{DT}{}^\alpha(\tau)$. They are rational numbers which `count' both $\tau$-stable and $\tau$-semistable coherent sheaves with Chern character $\alpha$ on $X$; strictly $\tau$-semistable sheaves must be counted with complicated rational weights. The $\bar{DT}{}^\alpha(\tau)$ are defined for all classes $\alpha$, and are equal to $DT^\alpha(\tau)$ when it is defined. They are unchanged under deformations of $X$, and transform by a wall-crossing formula under change of stability condition $\tau$. To prove all this, the authors study the local structure of the moduli stack $\mathfrak M$ of coherent sheaves on $X$. They show that an atlas for $\mathfrak M$ may be written locally as $\mathrm{Crit}(f)$ for $f:U\to{\mathbb C}$ holomorphic and $U$ smooth, and use this to deduce identities on the Behrend function $\nu_\mathfrak M$. They compute the invariants $\bar{DT}{}^\alpha(\tau)$ in examples, and make a conjecture about their integrality properties. They also extend the theory to abelian categories $\mathrm{mod}$-$\mathbb{C}Q\backslash I$ of representations of a quiver $Q$ with relations $I$ coming from a superpotential $W$ on $Q$.

LMSST: 24 Lectures on Elliptic Curves

Author : John William Scott Cassels
Publisher : Cambridge University Press
ISBN 13 : 9780521425308
Total Pages : 148 pages
Book Rating : 4.4/5 (253 download)

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Book Synopsis LMSST: 24 Lectures on Elliptic Curves by : John William Scott Cassels

Download or read book LMSST: 24 Lectures on Elliptic Curves written by John William Scott Cassels and published by Cambridge University Press. This book was released on 1991-11-21 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introductory text for beginning graduate students that is contemporary in approach without ignoring historical matters.

Physics Briefs

Author :
Publisher :
ISBN 13 :
Total Pages : 568 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Physics Briefs by :

Download or read book Physics Briefs written by and published by . This book was released on 1994 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields

Author : Lisa Berger
Publisher : American Mathematical Soc.
ISBN 13 : 1470442191
Total Pages : 144 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields by : Lisa Berger

Download or read book Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields written by Lisa Berger and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $mathbb F_p(t)$, when $p$ is prime and $rge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $mathbb F_q(t^1/d)$.

Theory of the Inhomogeneous Electron Gas

Author : Stig Lundqvist
Publisher : Springer Science & Business Media
ISBN 13 : 1489904158
Total Pages : 405 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Theory of the Inhomogeneous Electron Gas by : Stig Lundqvist

Download or read book Theory of the Inhomogeneous Electron Gas written by Stig Lundqvist and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of the inhomogeneous electron gas had its origin in the Thomas Fermi statistical theory, which is discussed in the first chapter of this book. This already leads to significant physical results for the binding energies of atomic ions, though because it leaves out shell structure the results of such a theory cannot reflect the richness of the Periodic Table. Therefore, for a long time, the earlier method proposed by Hartree, in which each electron is assigned its own personal wave function and energy, dominated atomic theory. The extension of the Hartree theory by Fock, to include exchange, had its parallel in the density description when Dirac showed how to incorporate exchange in the Thomas-Fermi theory. Considerably later, in 1951, Slater, in an important paper, showed how a result similar to but not identical with that of Dirac followed as a simplification of the Hartree-Fock method. It was Gombas and other workers who recognized that one could also incorporate electron correlation consistently into the Thomas-Fermi-Dirac theory by using uniform electron gas relations locally, and progress had been made along all these avenues by the 1950s.

Recent Progress in Mathematics

Author : Nam-Gyu Kang
Publisher : Springer Nature
ISBN 13 : 9811937087
Total Pages : 206 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Recent Progress in Mathematics by : Nam-Gyu Kang

Download or read book Recent Progress in Mathematics written by Nam-Gyu Kang and published by Springer Nature. This book was released on 2022-09-30 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of five chapters presenting problems of current research in mathematics, with its history and development, current state, and possible future direction. Four of the chapters are expository in nature while one is based more directly on research. All deal with important areas of mathematics, however, such as algebraic geometry, topology, partial differential equations, Riemannian geometry, and harmonic analysis. This book is addressed to researchers who are interested in those subject areas. Young-Hoon Kiem discusses classical enumerative geometry before string theory and improvements after string theory as well as some recent advances in quantum singularity theory, Donaldson–Thomas theory for Calabi–Yau 4-folds, and Vafa–Witten invariants. Dongho Chae discusses the finite-time singularity problem for three-dimensional incompressible Euler equations. He presents Kato's classical local well-posedness results, Beale–Kato–Majda's blow-up criterion, and recent studies on the singularity problem for the 2D Boussinesq equations. Simon Brendle discusses recent developments that have led to a complete classification of all the singularity models in a three-dimensional Riemannian manifold. He gives an alternative proof of the classification of noncollapsed steady gradient Ricci solitons in dimension 3. Hyeonbae Kang reviews some of the developments in the Neumann–Poincare operator (NPO). His topics include visibility and invisibility via polarization tensors, the decay rate of eigenvalues and surface localization of plasmon, singular geometry and the essential spectrum, analysis of stress, and the structure of the elastic NPO. Danny Calegari provides an explicit description of the shift locus as a complex of spaces over a contractible building. He describes the pieces in terms of dynamically extended laminations and of certain explicit “discriminant-like” affine algebraic varieties.