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Period Functions For Maass Wave Forms And Cohomology
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Book Synopsis Period Functions for Maass Wave Forms and Cohomology by : R. Bruggeman
Download or read book Period Functions for Maass Wave Forms and Cohomology written by R. Bruggeman and published by American Mathematical Soc.. This book was released on 2015-08-21 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors construct explicit isomorphisms between spaces of Maass wave forms and cohomology groups for discrete cofinite groups Γ⊂PSL2(R). In the case that Γ is the modular group PSL2(Z) this gives a cohomological framework for the results in Period functions for Maass wave forms. I, of J. Lewis and D. Zagier in Ann. Math. 153 (2001), 191-258, where a bijection was given between cuspidal Maass forms and period functions. The authors introduce the concepts of mixed parabolic cohomology group and semi-analytic vectors in principal series representation. This enables them to describe cohomology groups isomorphic to spaces of Maass cusp forms, spaces spanned by residues of Eisenstein series, and spaces of all Γ-invariant eigenfunctions of the Laplace operator. For spaces of Maass cusp forms the authors also describe isomorphisms to parabolic cohomology groups with smooth coefficients and standard cohomology groups with distribution coefficients. They use the latter correspondence to relate the Petersson scalar product to the cup product in cohomology.
Book Synopsis On the Theory of Maass Wave Forms by : Tobias Mühlenbruch
Download or read book On the Theory of Maass Wave Forms written by Tobias Mühlenbruch and published by Springer Nature. This book was released on 2020-05-06 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a rigorous analytical treatment of the theory of Maass wave forms. Readers will find this unified presentation invaluable, as it treats Maass wave forms as the central area of interest. Subjects at the cutting edge of research are explored in depth, such as Maass wave forms of real weight and the cohomology attached to Maass wave forms and transfer operators. Because Maass wave forms are given a deep exploration, this book offers an indispensable resource for those entering the field. Early chapters present a brief introduction to the theory of classical modular forms, with an emphasis on objects and results necessary to fully understand later material. Chapters 4 and 5 contain the book’s main focus: L-functions and period functions associated with families of Maass wave forms. Other topics include Maass wave forms of real weight, Maass cusp forms, and weak harmonic Maass wave forms. Engaging exercises appear throughout the book, with solutions available online. On the Theory of Maass Wave Forms is ideal for graduate students and researchers entering the area. Readers in mathematical physics and other related disciplines will find this a useful reference as well. Knowledge of complex analysis, real analysis, and abstract algebra is required.
Book Synopsis Holomorphic Automorphic Forms and Cohomology by : Roelof Bruggeman
Download or read book Holomorphic Automorphic Forms and Cohomology written by Roelof Bruggeman and published by American Mathematical Soc.. This book was released on 2018-05-29 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume by : Roelof Bruggeman
Download or read book Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume written by Roelof Bruggeman and published by American Mathematical Society. This book was released on 2023-07-31 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Modular Forms written by Henri Cohen and published by American Mathematical Soc.. This book was released on 2017-08-02 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and “fun” subject in itself and abounds with an amazing number of surprising identities. This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. After a number of motivating examples such as elliptic functions and theta functions, the modular group, its subgroups, and general aspects of holomorphic and nonholomorphic modular forms are explained, with an emphasis on explicit examples. The heart of the book is the classical theory developed by Hecke and continued up to the Atkin–Lehner–Li theory of newforms and including the theory of Eisenstein series, Rankin–Selberg theory, and a more general theory of theta series including the Weil representation. The final chapter explores in some detail more general types of modular forms such as half-integral weight, Hilbert, Jacobi, Maass, and Siegel modular forms. Some “gems” of the book are an immediately implementable trace formula for Hecke operators, generalizations of Haberland's formulas for the computation of Petersson inner products, W. Li's little-known theorem on the diagonalization of the full space of modular forms, and explicit algorithms due to the second author for computing Maass forms. This book is essentially self-contained, the necessary tools such as gamma and Bessel functions, Bernoulli numbers, and so on being given in a separate chapter.
Book Synopsis Igusa's $p$-Adic Local Zeta Function and the Monodromy Conjecture for Non-Degenerate Surface Singularities by : Bart Bories
Download or read book Igusa's $p$-Adic Local Zeta Function and the Monodromy Conjecture for Non-Degenerate Surface Singularities written by Bart Bories and published by American Mathematical Soc.. This book was released on 2016-06-21 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 2011 Lemahieu and Van Proeyen proved the Monodromy Conjecture for the local topological zeta function of a non-degenerate surface singularity. The authors start from their work and obtain the same result for Igusa's p-adic and the motivic zeta function. In the p-adic case, this is, for a polynomial f∈Z[x,y,z] satisfying f(0,0,0)=0 and non-degenerate with respect to its Newton polyhedron, we show that every pole of the local p-adic zeta function of f induces an eigenvalue of the local monodromy of f at some point of f−1(0)⊂C3 close to the origin. Essentially the entire paper is dedicated to proving that, for f as above, certain candidate poles of Igusa's p-adic zeta function of f, arising from so-called B1-facets of the Newton polyhedron of f, are actually not poles. This turns out to be much harder than in the topological setting. The combinatorial proof is preceded by a study of the integral points in three-dimensional fundamental parallelepipeds. Together with the work of Lemahieu and Van Proeyen, this main result leads to the Monodromy Conjecture for the p-adic and motivic zeta function of a non-degenerate surface singularity.
Book Synopsis The Conference on L-Functions by : Lin Weng
Download or read book The Conference on L-Functions written by Lin Weng and published by World Scientific. This book was released on 2007 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable volume collects papers written by many of the world's top experts on L-functions. It not only covers a wide range of topics from algebraic and analytic number theories, automorphic forms, to geometry and mathematical physics, but also treats the theory as a whole. The contributions reflect the latest, most advanced and most important aspects of L-functions. In particular, it contains Hida's lecture notes at the conference and at the Eigenvariety semester in Harvard University and Weng's detailed account of his works on high rank zeta functions and non-abelian L-functions.
Book Synopsis Higher Moments of Banach Space Valued Random Variables by : Svante Janson
Download or read book Higher Moments of Banach Space Valued Random Variables written by Svante Janson and published by American Mathematical Soc.. This book was released on 2015-10-27 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors define the :th moment of a Banach space valued random variable as the expectation of its :th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. The authors study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.
Book Synopsis On Non-Topological Solutions of the $A_{2}$ and $B_{2}$ Chern-Simons System by : Weiwei Ao
Download or read book On Non-Topological Solutions of the $A_{2}$ and $B_{2}$ Chern-Simons System written by Weiwei Ao and published by American Mathematical Soc.. This book was released on 2016-01-25 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Click here to view the abstract. IntroductionProof of Theorem 1.1 in the caseProof of Theorem 1.1 in the caseAppendixBibliography
Book Synopsis Global Carleman Estimates for Degenerate Parabolic Operators with Applications by : P. Cannarsa
Download or read book Global Carleman Estimates for Degenerate Parabolic Operators with Applications written by P. Cannarsa and published by American Mathematical Soc.. This book was released on 2016-01-25 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Degenerate parabolic operators have received increasing attention in recent years because they are associated with both important theoretical analysis, such as stochastic diffusion processes, and interesting applications to engineering, physics, biology, and economics. This manuscript has been conceived to introduce the reader to global Carleman estimates for a class of parabolic operators which may degenerate at the boundary of the space domain, in the normal direction to the boundary. Such a kind of degeneracy is relevant to study the invariance of a domain with respect to a given stochastic diffusion flow, and appears naturally in climatology models.
Book Synopsis Moduli of Double EPW-Sextics by : Kieran G. O'Grady
Download or read book Moduli of Double EPW-Sextics written by Kieran G. O'Grady and published by American Mathematical Soc.. This book was released on 2016-03-10 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author studies the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of ⋀3C6 modulo the natural action of SL6, call it M. This is a compactification of the moduli space of smooth double EPW-sextics and hence birational to the moduli space of HK 4-folds of Type K3[2] polarized by a divisor of square 2 for the Beauville-Bogomolov quadratic form. The author will determine the stable points. His work bears a strong analogy with the work of Voisin, Laza and Looijenga on moduli and periods of cubic 4-folds.
Book Synopsis Irreducible Geometric Subgroups of Classical Algebraic Groups by : Timothy C. Burness,
Download or read book Irreducible Geometric Subgroups of Classical Algebraic Groups written by Timothy C. Burness, and published by American Mathematical Soc.. This book was released on 2016-01-25 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a non-trivial irreducible tensor-indecomposable -restricted rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where is a disconnected maximal positive-dimensional closed subgroup of preserving a natural geometric structure on .
Book Synopsis Classification of $E_0$-Semigroups by Product Systems by : Michael Skeide
Download or read book Classification of $E_0$-Semigroups by Product Systems written by Michael Skeide and published by American Mathematical Soc.. This book was released on 2016-03-10 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these notes the author presents a complete theory of classification of E0-semigroups by product systems of correspondences. As an application of his theory, he answers the fundamental question if a Markov semigroup admits a dilation by a cocycle perturbations of noise: It does if and only if it is spatial.
Book Synopsis Stability of Line Solitons for the KP-II Equation in $\mathbb {R}^2$ by : Tetsu Mizumachi
Download or read book Stability of Line Solitons for the KP-II Equation in $\mathbb {R}^2$ written by Tetsu Mizumachi and published by American Mathematical Soc.. This book was released on 2015-10-27 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author proves nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as . He finds that the amplitude of the line soliton converges to that of the line soliton at initial time whereas jumps of the local phase shift of the crest propagate in a finite speed toward . The local amplitude and the phase shift of the crest of the line solitons are described by a system of 1D wave equations with diffraction terms.
Book Synopsis Faithfully Quadratic Rings by : M. Dickmann
Download or read book Faithfully Quadratic Rings written by M. Dickmann and published by American Mathematical Soc.. This book was released on 2015-10-27 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where is not a sum of squares and is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of -isometry, where is a preorder of the given ring, , or . (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in the field case.
Book Synopsis Classes of Polish Spaces Under Effective Borel Isomorphism by : Vassilios Gregoriades
Download or read book Classes of Polish Spaces Under Effective Borel Isomorphism written by Vassilios Gregoriades and published by American Mathematical Soc.. This book was released on 2016-03-10 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author studies the equivalence classes under Δ11 isomorphism, otherwise effective Borel isomorphism, between complete separable metric spaces which admit a recursive presentation and he shows the existence of strictly increasing and strictly decreasing sequences as well as of infinite antichains under the natural notion of Δ11-reduction, as opposed to the non-effective case, where only two such classes exist, the one of the Baire space and the one of the naturals.
Book Synopsis Stability of KAM Tori for Nonlinear Schrödinger Equation by : Hongzi Cong
Download or read book Stability of KAM Tori for Nonlinear Schrödinger Equation written by Hongzi Cong and published by American Mathematical Soc.. This book was released on 2016-01-25 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors prove the long time stability of KAM tori (thus quasi-periodic solutions) for nonlinear Schrödinger equation subject to Dirichlet boundary conditions , where is a real Fourier multiplier. More precisely, they show that, for a typical Fourier multiplier , any solution with the initial datum in the -neighborhood of a KAM torus still stays in the -neighborhood of the KAM torus for a polynomial long time such as for any given with , where is a constant depending on and as .
