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Forms Of Fermat Equations And Their Zeta Functions
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Book Synopsis Forms of Fermat Equations and Their Zeta Functions by : Lars Brnjes
Download or read book Forms of Fermat Equations and Their Zeta Functions written by Lars Brnjes and published by World Scientific. This book was released on 2004 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, an abstract theory of oOe1/4 formsoOe1/4Oao is developed, thus providing a conceptually satisfying framework for the classification of forms of Fermat equations. The classical results on diagonal forms are extended to the broader class of all forms of Fermat varieties."
Book Synopsis Forms of Fermat Equations and Their Zeta Functions by : Lars Brnjes
Download or read book Forms of Fermat Equations and Their Zeta Functions written by Lars Brnjes and published by World Scientific. This book was released on 2004 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, an abstract theory of 'forms' is developed, thus providing a conceptually satisfying framework for the classification of forms of Fermat equations. The classical results on diagonal forms are extended to the broader class of all forms of Fermat varieties.The main topic is the study of forms of the Fermat equation over an arbitrary field K. Using Galois descent, all such forms are classified; particularly, a complete and explicit classification of all cubic binary equations is given. If K is a finite field containing the d-th roots of unity, the Galois representation on l-adic cohomology (and so in particular the zeta function) of the hypersurface associated with an arbitrary form of the Fermat equation of degree d is computed.
Book Synopsis Zeta Functions over Zeros of Zeta Functions by : André Voros
Download or read book Zeta Functions over Zeros of Zeta Functions written by André Voros and published by Springer Science & Business Media. This book was released on 2009-11-21 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, the famous zeros of the Riemann zeta function and its generalizations (L-functions, Dedekind and Selberg zeta functions)are analyzed through several zeta functions built over those zeros.
Book Synopsis Zeta Functions of Reductive Groups and Their Zeros by : Lin Weng
Download or read book Zeta Functions of Reductive Groups and Their Zeros written by Lin Weng and published by World Scientific Publishing Company. This book was released on 2018 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Zeta Functions in Algebra and Geometry by : Antonio Campillo
Download or read book Zeta Functions in Algebra and Geometry written by Antonio Campillo and published by American Mathematical Soc.. This book was released on 2012 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the Second International Workshop on Zeta Functions in Algebra and Geometry held May 3-7, 2010 at the Universitat de les Illes Balears, Palma de Mallorca, Spain. The conference focused on the following topics: arithmetic and geometric aspects of local, topological, and motivic zeta functions, Poincare series of valuations, zeta functions of groups, rings, and representations, prehomogeneous vector spaces and their zeta functions, and height zeta functions.
Book Synopsis Modular Forms and Fermat’s Last Theorem by : Gary Cornell
Download or read book Modular Forms and Fermat’s Last Theorem written by Gary Cornell and published by Springer Science & Business Media. This book was released on 1997 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held at Boston University. The purpose of the conference, and indeed this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof, and to explain how his result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by reflecting on the history of the problem, while placing Wiles' theorem into a more general Diophantine context suggesting future applications.
Book Synopsis The Riemann Zeta-Function by : Anatoly A. Karatsuba
Download or read book The Riemann Zeta-Function written by Anatoly A. Karatsuba and published by Walter de Gruyter. This book was released on 2011-05-03 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
Book Synopsis Zeta and Q-Zeta Functions and Associated Series and Integrals by : H. M. Srivastava
Download or read book Zeta and Q-Zeta Functions and Associated Series and Integrals written by H. M. Srivastava and published by Elsevier. This book was released on 2011-10-25 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book will be invaluable because it covers not only detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions, but stimulating historical accounts of a large number of problems and well-classified tables of series and integrals. Detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions
Book Synopsis Series Associated with the Zeta and Related Functions by : Hari M. Srivastava
Download or read book Series Associated with the Zeta and Related Functions written by Hari M. Srivastava and published by Springer. This book was released on 2001 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been an increasing interest in problems involving closed form evaluations of (and representations of the Riemann Zeta function at positive integer arguments as) various families of series associated with the Riemann Zeta function ((s), the Hurwitz Zeta function ((s,a), and their such extensions and generalizations as (for example) Lerch's transcendent (or the Hurwitz-Lerch Zeta function) iI>(z, s, a). Some of these developments have apparently stemmed from an over two-century-old theorem of Christian Goldbach (1690-1764), which was stated in a letter dated 1729 from Goldbach to Daniel Bernoulli (1700-1782), from recent rediscoveries of a fairly rapidly convergent series representation for ((3), which is actually contained in a 1772 paper by Leonhard Euler (1707-1783), and from another known series representation for ((3), which was used by Roger Apery (1916-1994) in 1978 in his celebrated proof of the irrationality of ((3). This book is motivated essentially by the fact that the theories and applications of the various methods and techniques used in dealing with many different families of series associated with the Riemann Zeta function and its aforementioned relatives are to be found so far only"in widely scattered journal articles. Thus our systematic (and unified) presentation of these results on the evaluation and representation of the Zeta and related functions is expected to fill a conspicuous gap in the existing books dealing exclusively with these Zeta functions.
Book Synopsis Exploring the Riemann Zeta Function by : Hugh Montgomery
Download or read book Exploring the Riemann Zeta Function written by Hugh Montgomery and published by Springer. This book was released on 2017-09-11 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects. The book focuses on both old and new results towards the solution of long-standing problems as well as it features some key historical remarks. The purpose of this volume is to present in a unified way broad and deep areas of research in a self-contained manner. It will be particularly useful for graduate courses and seminars as well as it will make an excellent reference tool for graduate students and researchers in Mathematics, Mathematical Physics, Engineering and Cryptography.
Book Synopsis Number Theoretic Methods by : Shigeru Kanemitsu
Download or read book Number Theoretic Methods written by Shigeru Kanemitsu and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the very successful second China-Japan Seminar held in lizuka, Fukuoka, Japan, during March 12-16, 2001 under the support of the Japan Society for the Promotion of Science (JSPS) and the National Science Foundation of China (NSFC), and some invited papers of eminent number-theorists who visited Japan during 1999-2001 at the occasion of the Conference at the Research Institute of Mathematical Sciences (RIMS), Kyoto University. The proceedings of the 1st China-Japan Seminar held in September 1999 in Beijing has been published recently {2002) by Kluwer as DEVM 6 which also contains some invited papers. The topics of that volume are, however, restricted to analytic number theory and many papers in this field are assembled. In this volume, we return to the lines of the previous one "Number Theory and its Applications", published as DEVM 2 by Kluwer in 1999 and uphold the spirit of presenting various topics in number theory and related areas with possible applica tions, in a unified manner, and this time in nearly a book form with a well-prepared index. We accomplish this task by collecting highly informative and readable survey papers (including half-survey type papers), giving overlooking surveys of the hith erto obtained results in up-to-the-hour form with insight into the new developments, which are then analytically continued to a collection of high standard research papers which are concerned with rather diversed areas and will give good insight into new researches in the new century.
Book Synopsis History of Zeta Functions by : Robert Spira
Download or read book History of Zeta Functions written by Robert Spira and published by . This book was released on 1999 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Local Zeta Functions Attached to the Minimal Spherical Series for a Class of Symmetric Spaces by : Nicole Bopp
Download or read book Local Zeta Functions Attached to the Minimal Spherical Series for a Class of Symmetric Spaces written by Nicole Bopp and published by American Mathematical Soc.. This book was released on 2005 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this paper is to prove a functional equation for a local zeta function attached to the minimal spherical series for a class of real reductive symmetric spaces. These symmetric spaces are obtained as follows. We consider a graded simple real Lie algebra $\widetilde{\mathfrak g}$ of the form $\widetilde{\mathfrak g}=V^-\oplus \mathfrak g\oplus V^+$, where $[\mathfrak g,V^+]\subset V^+$, $[\mathfrak g,V^-]\subset V^-$ and $[V^-,V^+]\subset \mathfrak g$. If the graded algebra is regular, then a suitable group $G$ with Lie algebra $\mathfrak g$ has a finite number of open orbits in $V^+$, each of them is a realization of a symmetric space $G\slash H_p$.The functional equation gives a matrix relation between the local zeta functions associated to $H_p$-invariant distributions vectors for the same minimal spherical representation of $G$. This is a generalization of the functional equation obtained by Godement} and Jacquet for the local zeta function attached to a coefficient of a representation of $GL(n,\mathbb R)$.
Download or read book Number Theory written by Matti Jutila and published by Walter de Gruyter. This book was released on 2014-01-02 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Proceedings contain 22 refereed research and survey articles based on lectures given at the Turku Symposium on Number Theory in Memory of Kustaa Inkeri, held in Turku, Finland, from May 31 to June 4, 1999. The subject of the symposium was number theory in a broad sense with an emphasis on recent advances and modern methods. The topics covered in this volume include various questions in elementary number theory, new developments in classical Diophantine problems - in particular of the Fermat and Catalan type, the ABC-conjecture, arithmetic algebraic geometry, elliptic curves, Diophantine approximations, Abelian fields, exponential sums, sieve methods, box splines, the Riemann zeta-function and other Dirichlet series, and the spectral theory of automorphic functions with its arithmetical applications.
Author :Antanas Laurincikas Publisher :Springer Science & Business Media ISBN 13 :9781402010149 Total Pages :202 pages Book Rating :4.0/5 (11 download)
Book Synopsis The Lerch zeta-function by : Antanas Laurincikas
Download or read book The Lerch zeta-function written by Antanas Laurincikas and published by Springer Science & Business Media. This book was released on 2002 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a generalization of the classic Riemann, and Hurwitz zeta-functions, containing both analytic and probability theory of Lerch zeta-functions.
Book Synopsis First European Congress of Mathematics Paris, July 6–10, 1992 by : Anthony Joseph
Download or read book First European Congress of Mathematics Paris, July 6–10, 1992 written by Anthony Joseph and published by Birkhäuser. This book was released on 2012-12-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of Contents: D. Duffie: Martingales, Arbitrage, and Portfolio Choice J. Frhlich: Mathematical Aspects of the Quantum Hall Effect M. Giaquinta: Analytic and Geometric Aspects of Variational Problems for Vector Valued Mappings U. Hamenstdt: Harmonic Measures for Leafwise Elliptic Operators Along Foliations M. Kontsevich: Feynman Diagrams and Low-Dimensional Topology S.B. Kuksin: KAM-Theory for Partial Differential Equations M. Laczkovich: Paradoxical Decompositions: A Survey of Recent Results J.-F. Le Gall: A Path-Valued Markov Process and its Connections with Partial Differential Equations I. Madsen: The Cyclotomic Trace in Algebraic K-Theory A.S. Merkurjev: Algebraic K-Theory and Galois Cohomology J. Nekovr: Values of L-Functions and p-Adic Cohomology Y.A. Neretin: Mantles, Trains and Representations of Infinite Dimensional Groups M.A. Nowak: The Evolutionary Dynamics of HIV Infections R. Piene: On the Enumeration of Algebraic Curves - from Circles to Instantons A. Quarteroni: Mathematical Aspects of Domain Decomposition Methods A. Schrijver: Paths in Graphs and Curves on Surfaces B. Silverman: Function Estimation and Functional Data Analysis V. Strassen: Algebra and Complexity P. Tukia: Generalizations of Fuchsian and Kleinian Groups C. Viterbo: Properties of Embedded Lagrange Manifolds D. Voiculescu: Alternative Entropies in Operator Algebras M. Wodzicki : Algebraic K-Theory and Functional Analysis D. Zagier: Values of Zeta Functions and Their Applications.
Book Synopsis Selberg Zeta and Theta Functions by : Ulrich Bunke
Download or read book Selberg Zeta and Theta Functions written by Ulrich Bunke and published by De Gruyter Akademie Forschung. This book was released on 1995 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give a self contained exposition of the theory of Selberg zeta and theta functions for bundles on compact locally symmetric spaces of rank 1. The connection between these functions and the spectrum of certain elliptic differential operators is provided by a version of the Selberg trace formula. The theta function is a regularized trace of the wave group. Originally defined geometrically, the Selberg zeta function has a representation in terms of regularized determinants. This leads to a complete description of its singularities. These results are employed in order to establish a functional equation and further properties of the Ruelle zeta function. A couple of explicit examples is worked out. Additional chapters are devoted to the theta function of Riemannian surfaces with cusps and to alternative descriptions of the singularities of the Selberg zeta function in terms of Lie algebra and group cohomology.
