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Partition Functions and Automorphic Forms

Partition Functions and Automorphic Forms
Author: Valery A. Gritsenko
Publisher: Springer Nature
Total Pages: 422
Release: 2020-07-09
Genre: Mathematics
ISBN: 3030424006
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This book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to quantum gravity, 3) superconformal indices and elliptic hypergeometric integrals, related instanton partition functions, 4) moonshine, its arithmetic aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. All the topics covered are related to various partition functions emerging in different supersymmetric and ordinary quantum field theories in curved space-times of different (d=2,3,...,6) dimensions. Presenting multidisciplinary methods (localization, Borcherds products, theory of special functions, Cremona maps, etc) for treating a range of partition functions, the book is intended for graduate students and young postdocs interested in the interaction between quantum field theory and mathematics related to automorphic forms, representation theory, number theory and geometry, and mirror symmetry.

Modular And Automorphic Forms & Beyond

Modular And Automorphic Forms & Beyond
Author: Hossein Movasati
Publisher: World Scientific
Total Pages: 323
Release: 2021-10-12
Genre: Mathematics
ISBN: 9811238693
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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'.

Multiple Dirichlet Series, L-functions and Automorphic Forms

Multiple Dirichlet Series, L-functions and Automorphic Forms
Author: Daniel Bump
Publisher: Springer
Total Pages: 367
Release: 2012-07-09
Genre: Mathematics
ISBN: 0817683348
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Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibits surprising and deep connections to crystal graphs and mathematical physics. As such, it represents a new way in which areas including number theory, combinatorics, statistical mechanics, and quantum groups are seen to fit together. The volume also includes papers on automorphic forms and L-functions and related number-theoretic topics. This volume will be a valuable resource for graduate students and researchers in number theory, combinatorics, representation theory, mathematical physics, and special functions. Contributors: J. Beineke, B. Brubaker, D. Bump, G. Chinta, G. Cornelissen, C.A. Diaconu, S. Frechette, S. Friedberg, P. Garrett, D. Goldfeld, P.E. Gunnells, B. Heim, J. Hundley, D. Ivanov, Y. Komori, A.V. Kontorovich, O. Lorscheid, K. Matsumoto, P.J. McNamara, S.J. Patterson, M. Suzuki, H. Tsumura.

L-Functions and Automorphic Forms

L-Functions and Automorphic Forms
Author: Jan Hendrik Bruinier
Publisher: Springer
Total Pages: 367
Release: 2018-02-22
Genre: Mathematics
ISBN: 3319697129
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This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "Automorphic Forms and L-Functions", held at the University of Heidelberg in 2016. The theory of automorphic forms and their associated L-functions is one of the central research areas in modern number theory, linking number theory, arithmetic geometry, representation theory, and complex analysis in many profound ways. The 19 papers cover a wide range of topics within the scope of the conference, including automorphic L-functions and their special values, p-adic modular forms, Eisenstein series, Borcherds products, automorphic periods, and many more.

Conformal Field Theory, Automorphic Forms and Related Topics

Conformal Field Theory, Automorphic Forms and Related Topics
Author: Winfried Kohnen
Publisher: Springer
Total Pages: 370
Release: 2014-08-22
Genre: Mathematics
ISBN: 3662438313
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This book, part of the series Contributions in Mathematical and Computational Sciences, reviews recent developments in the theory of vertex operator algebras (VOAs) and their applications to mathematics and physics. The mathematical theory of VOAs originated from the famous monstrous moonshine conjectures of J.H. Conway and S.P. Norton, which predicted a deep relationship between the characters of the largest simple finite sporadic group, the Monster and the theory of modular forms inspired by the observations of J. MacKay and J. Thompson. The contributions are based on lectures delivered at the 2011 conference on Conformal Field Theory, Automorphic Forms and Related Topics, organized by the editors as part of a special program offered at Heidelberg University that summer under the sponsorship of the Mathematics Center Heidelberg (MATCH).

Modular Functions and Dirichlet Series in Number Theory

Modular Functions and Dirichlet Series in Number Theory
Author: Tom M. Apostol
Publisher: Springer Science & Business Media
Total Pages: 218
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461209994
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A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series.

Partitions, q-Series, and Modular Forms

Partitions, q-Series, and Modular Forms
Author: Krishnaswami Alladi
Publisher: Springer Science & Business Media
Total Pages: 233
Release: 2011-11-01
Genre: Mathematics
ISBN: 1461400287
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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.

Arithmetic of Partition Functions and Q-combinatorics

Arithmetic of Partition Functions and Q-combinatorics
Author: Byung Chan Kim
Publisher:
Total Pages:
Release: 2010
Genre:
ISBN:
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Integer partitions play important roles in diverse areas of mathematics such as q-series, the theory of modular forms, representation theory, symmetric functions and mathematical physics. Among these, we study the arithmetic of partition functions and q-combinatorics via bijective methods, q-series and modular forms. In particular, regarding arithmetic properties of partition functions, we examine partition congruences of the overpartition function and cubic partition function and inequalities involving t-core partitions. Concerning q-combinatorics, we establish various combinatorial proofs for q-series identities appearing in Ramanujan's lost notebook and give combinatorial interpretations for third and sixth order mock theta functions.

Generalized Frobenius Partitions

Generalized Frobenius Partitions
Author: George E. Andrews
Publisher: American Mathematical Soc.
Total Pages: 50
Release: 1984
Genre: Mathematics
ISBN: 0821823027
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This paper is devoted to the study of equilength two-line arrays of non-negative integers. These are called generalized Frobenius partitions. It is shown that such objects have numerous interactions with modular forms, Kloosterman quadratic forms, the Lusztig-Macdonald-Wall conjectures as well as with classical theta functions and additive number theory.