Automorphic Forms And Even Unimodular Lattices
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Automorphic Forms And Even Unimodular Lattices
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Author : Gaëtan Chenevier
language : en
Publisher: Springer
Release Date : 2019-02-28
Automorphic Forms And Even Unimodular Lattices written by Gaëtan Chenevier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-28 with Mathematics categories.
This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur. Its connecting thread is a question about lattices of rank 24: the problem of p-neighborhoods between Niemeier lattices. This question, whose expression is quite elementary, is in fact very natural from the automorphic point of view, and turns out to be surprisingly intriguing. We explain how the new advances in the Langlands program mentioned above pave the way for a solution. This study proves to be very rich, leading us to classical themes such as theta series, Siegel modular forms, the triality principle, L-functions and congruences between Galois representations. This monograph is intended for any mathematician with an interest in Euclidean lattices, automorphic forms or number theory. A large part of it is meant to be accessible to non-specialists.
Positive Definite Unimodular Lattices With Trivial Automorphism Groups
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Author : Etsuko Bannai
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Positive Definite Unimodular Lattices With Trivial Automorphism Groups written by Etsuko Bannai and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
The existence of lattices with trivial automorphism group was shown by O'Meara, who gave an algorithm to construct such a lattice starting from any given lattice. In this process, the discriminants of the lattices increase in each step. Biermann proved the existence of a lattice with trivial automorphism group in every genus of positive definite integral lattices of any dimension with sufficiently large discriminant. In his proof the fact that the discriminant is very large is crucial. We are, instead, interested in lattices with small discriminant.
Automorphic Forms And Zeta Functions
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Author : Siegfried Bcherer
language : en
Publisher: World Scientific
Release Date : 2006
Automorphic Forms And Zeta Functions written by Siegfried Bcherer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This volume contains a valuable collection of articles presented at a conference on Automorphic Forms and Zeta Functions in memory of Tsuneo Arakawa, an eminent researcher in modular forms in several variables and zeta functions. The book begins with a review of his works, followed by 16 articles by experts in the fields including H Aoki, R Berndt, K Hashimoto, S Hayashida, Y Hironaka, H Katsurada, W Kohnen, A Krieg, A Murase, H Narita, T Oda, B Roberts, R Schmidt, R Schulze-Pillot, N Skoruppa, T Sugano, and D Zagier. A variety of topics in the theory of modular forms and zeta functions are covered: Theta series and the basis problems, Jacobi forms, automorphic forms on Sp(1, q), double zeta functions, special values of zeta and L -functions, many of which are closely related to Arakawa''s works. This collection of papers illustrates Arakawa''s contributions and the current trends in modular forms in several variables and related zeta functions. Contents: Tsuneo Arakawa and His Works; Estimate of the Dimensions of Hilbert Modular Forms by Means of Differential Operators (H Aoki); MarsdenOCoWeinstein Reduction, Orbits and Representations of the Jacobi Group (R Berndt); On Eisenstein Series of Degree Two for Squarefree Levels and the Genus Version of the Basis Problem I (S BAcherer); Double Zeta Values and Modular Forms (H Gangl et al.); Type Numbers and Linear Relations of Theta Series for Some General Orders of Quaternion Algebras (K-I Hashimoto); Skew-Holomorphic Jacobi Forms of Higher Degree (S Hayashida); A Hermitian Analog of the Schottky Form (M Hentschel & A Krieg); The Siegel Series and Spherical Functions on O (2 n) / (O (n) x O (n) ) (Y Hironaka & F Sato); KoecherOCoMaa Series for Real Analytic Siegel Eisenstein Series (T Ibukiyama & H Katsurada); A Short History on Investigation of the Special Values of Zeta and L -Functions of Totally Real Number Fields (T Ishii & T Oda); Genus Theta Series, Hecke Operators and the Basis Problem for Eisenstein Series (H Katsurada & R Schulze-Pillot); The Quadratic Mean of Automorphic L -Functions (W Kohnen et al.); Inner Product Formula for Kudla Lift (A Murase & T Sugano); On Certain Automorphic Forms of Sp (1, q ) (Arakawa''s Results and Recent Progress) (H-A Narita); On Modular Forms for the Paramodular Groups (B Roberts & R Schmidt); SL(2, Z)-Invariant Spaces Spanned by Modular Units (N-P Skoruppa & W Eholzer). Readership: Researchers and graduate students in number theory or representation theory as well as in mathematical physics or combinatorics."
Automorphic Forms And Zeta Functions Proceedings Of The Conference In Memory Of Tsuneo Arakawa
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Author : Masanobu Kaneko
language : en
Publisher: World Scientific
Release Date : 2006-01-03
Automorphic Forms And Zeta Functions Proceedings Of The Conference In Memory Of Tsuneo Arakawa written by Masanobu Kaneko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-03 with Mathematics categories.
This volume contains a valuable collection of articles presented at a conference on Automorphic Forms and Zeta Functions in memory of Tsuneo Arakawa, an eminent researcher in modular forms in several variables and zeta functions. The book begins with a review of his works, followed by 16 articles by experts in the fields including H Aoki, R Berndt, K Hashimoto, S Hayashida, Y Hironaka, H Katsurada, W Kohnen, A Krieg, A Murase, H Narita, T Oda, B Roberts, R Schmidt, R Schulze-Pillot, N Skoruppa, T Sugano, and D Zagier. A variety of topics in the theory of modular forms and zeta functions are covered: Theta series and the basis problems, Jacobi forms, automorphic forms on Sp(1, q), double zeta functions, special values of zeta and L-functions, many of which are closely related to Arakawa's works.This collection of papers illustrates Arakawa's contributions and the current trends in modular forms in several variables and related zeta functions.
Self Dual Codes And Invariant Theory
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Author : Gabriele Nebe
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-09
Self Dual Codes And Invariant Theory written by Gabriele Nebe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-09 with Mathematics categories.
One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory, which has inspired hundreds of papers about generalizations and applications of this theorem to different types of codes. This self-contained book develops a new theory which is powerful enough to include all the earlier generalizations.
Families Of Automorphic Forms
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Author : Roelof W. Bruggeman
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-02-28
Families Of Automorphic Forms written by Roelof W. Bruggeman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-28 with Mathematics categories.
Automorphic forms on the upper half plane have been studied for a long time. Most attention has gone to the holomorphic automorphic forms, with numerous applications to number theory. Maass, [34], started a systematic study of real analytic automorphic forms. He extended Hecke’s relation between automorphic forms and Dirichlet series to real analytic automorphic forms. The names Selberg and Roelcke are connected to the spectral theory of real analytic automorphic forms, see, e. g. , [50], [51]. This culminates in the trace formula of Selberg, see, e. g. , Hejhal, [21]. Automorphicformsarefunctionsontheupperhalfplanewithaspecialtra- formation behavior under a discontinuous group of non-euclidean motions in the upper half plane. One may ask how automorphic forms change if one perturbs this group of motions. This question is discussed by, e. g. , Hejhal, [22], and Phillips and Sarnak, [46]. Hejhal also discusses the e?ect of variation of the multiplier s- tem (a function on the discontinuous group that occurs in the description of the transformation behavior of automorphic forms). In [5]–[7] I considered variation of automorphic forms for the full modular group under perturbation of the m- tiplier system. A method based on ideas of Colin de Verdi` ere, [11], [12], gave the meromorphic continuation of Eisenstein and Poincar ́ e series as functions of the eigenvalue and the multiplier system jointly. The present study arose from a plan to extend these results to much more general groups (discrete co?nite subgroups of SL (R)).
Automorphic Forms And Lie Superalgebras
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Author : Urmie Ray
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-06
Automorphic Forms And Lie Superalgebras written by Urmie Ray and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-06 with Mathematics categories.
This book provides the reader with the tools to understand the ongoing classification and construction project of Lie superalgebras. It presents the material in as simple terms as possible. Coverage specifically details Borcherds-Kac-Moody superalgebras. The book examines the link between the above class of Lie superalgebras and automorphic form and explains their construction from lattice vertex algebras. It also includes all necessary background information.
Modular And Automorphic Forms Beyond
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Author : Hossein Movasati
language : en
Publisher: World Scientific
Release Date : 2021-10-12
Modular And Automorphic Forms Beyond written by Hossein Movasati and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-12 with Mathematics categories.
The guiding principle in this monograph is to develop a new theory of modular forms which encompasses most of the available theory of modular forms in the literature, such as those for congruence groups, Siegel and Hilbert modular forms, many types of automorphic forms on Hermitian symmetric domains, Calabi-Yau modular forms, with its examples such as Yukawa couplings and topological string partition functions, and even go beyond all these cases. Its main ingredient is the so-called 'Gauss-Manin connection in disguise'.
Arithmetic And Geometry Of K3 Surfaces And Calabi Yau Threefolds
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Author : Radu Laza
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-12
Arithmetic And Geometry Of K3 Surfaces And Calabi Yau Threefolds written by Radu Laza and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-12 with Mathematics categories.
In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics—in particular, in string theory. The workshop on Arithmetic and Geometry of K3 surfaces and Calabi–Yau threefolds, held at the Fields Institute (August 16-25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi–Yau varieties. With the big variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi–Yau workshop started with 3 days of introductory lectures. A selection of 4 of these lectures is included in this volume. These lectures can be used as a starting point for the graduate students and other junior researchers, or as a guide to the subject.
Algebraic Combinatorics
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Author : Eiichi Bannai
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-02-22
Algebraic Combinatorics written by Eiichi Bannai and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-22 with Mathematics categories.
This series is devoted to the publication of high-level monographs which cover the whole spectrum of current discrete mathematics and its applications in various fields. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of discrete mathematics. Contributions which are on the borderline of discrete mathematics and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.