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Partition Functions and Automorphic Forms

2020-07-09 Mathematics
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Release : 2020-07-09
Genre : Mathematics
Kind : eBook
Book Rating : 006/5 ( reviews)

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Book Synopsis Partition Functions and Automorphic Forms by : Valery A. Gritsenko

Download or read book Partition Functions and Automorphic Forms written by Valery A. Gritsenko. This book was released on 2020-07-09. Available in PDF, EPUB and Kindle. Book excerpt: 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

2021-10-12 Mathematics
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Release : 2021-10-12
Genre : Mathematics
Kind : eBook
Book Rating : 693/5 ( reviews)

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Book Synopsis Modular And Automorphic Forms & Beyond by : Hossein Movasati

Download or read book Modular And Automorphic Forms & Beyond written by Hossein Movasati. This book was released on 2021-10-12. Available in PDF, EPUB and Kindle. Book excerpt: 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

2012-07-09 Mathematics
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Release : 2012-07-09
Genre : Mathematics
Kind : eBook
Book Rating : 348/5 ( reviews)

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Book Synopsis Multiple Dirichlet Series, L-functions and Automorphic Forms by : Daniel Bump

Download or read book Multiple Dirichlet Series, L-functions and Automorphic Forms written by Daniel Bump. This book was released on 2012-07-09. Available in PDF, EPUB and Kindle. Book excerpt: 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

2018-02-22 Mathematics
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Release : 2018-02-22
Genre : Mathematics
Kind : eBook
Book Rating : 129/5 ( reviews)

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Book Synopsis L-Functions and Automorphic Forms by : Jan Hendrik Bruinier

Download or read book L-Functions and Automorphic Forms written by Jan Hendrik Bruinier. This book was released on 2018-02-22. Available in PDF, EPUB and Kindle. Book excerpt: 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

2014-08-22 Mathematics
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Release : 2014-08-22
Genre : Mathematics
Kind : eBook
Book Rating : 313/5 ( reviews)

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Book Synopsis Conformal Field Theory, Automorphic Forms and Related Topics by : Winfried Kohnen

Download or read book Conformal Field Theory, Automorphic Forms and Related Topics written by Winfried Kohnen. This book was released on 2014-08-22. Available in PDF, EPUB and Kindle. Book excerpt: 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).

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