Expansion of Type Forms Into Fourier Series
Author: James Arthur Bender
Publisher:
Published: 1948
Total Pages: 98
ISBN-13:
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Fourier Coefficients of Automorphic Forms
Author: R. W. Bruggeman
Publisher: Springer
Published: 2006-11-15
Total Pages: 205
ISBN-13: 3540387269
DOWNLOAD EBOOKRepresentations of SU(2,1) in Fourier Term Modules
Author: Roelof W. Bruggeman
Publisher: Springer Nature
Published: 2023-11-06
Total Pages: 217
ISBN-13: 3031431928
DOWNLOAD EBOOKThis book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup. It considers the “abelian” Fourier term modules connected to characters of the maximal unipotent subgroups of SU(2,1), and also the “non-abelian” modules, described via theta functions. A complete description of the submodule structure of all Fourier term modules is given, with a discussion of the consequences for Fourier expansions of automorphic forms, automorphic forms with exponential growth included. These results can be applied to prove a completeness result for Poincaré series in spaces of square integrable automorphic forms. Aimed at researchers and graduate students interested in automorphic forms, harmonic analysis on Lie groups, and number-theoretic topics related to Poincaré series, the book will also serve as a basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed.
Geometric Applications of Fourier Series and Spherical Harmonics
Author: H. Groemer
Publisher: Cambridge University Press
Published: 1996-09-13
Total Pages: 343
ISBN-13: 0521473187
DOWNLOAD EBOOKThis book provides a comprehensive presentation of geometric results, primarily from the theory of convex sets, that have been proved by the use of Fourier series or spherical harmonics. An important feature of the book is that all necessary tools from the classical theory of spherical harmonics are presented with full proofs. These tools are used to prove geometric inequalities, stability results, uniqueness results for projections and intersections by hyperplanes or half-spaces and characterisations of rotors in convex polytopes. Again, full proofs are given. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets. This treatise will be welcomed both as an introduction to the subject and as a reference book for pure and applied mathematics.
The 1-2-3 of Modular Forms
Author: Jan Hendrik Bruinier
Publisher: Springer Science & Business Media
Published: 2008-02-10
Total Pages: 273
ISBN-13: 3540741194
DOWNLOAD EBOOKThis book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.
Introduction to Elliptic Curves and Modular Forms
Author: Neal I. Koblitz
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 262
ISBN-13: 1461209099
DOWNLOAD EBOOKThe theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer. This new edition details the current state of knowledge of elliptic curves.
Fourier Analysis and Approximation
Author: P.L. Butzer
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 565
ISBN-13: 3034874480
DOWNLOAD EBOOKAt the international conference on 'Harmonic Analysis and Integral Transforms', conducted by one of the authors at the Mathematical Research Institute in Oberwolfach (Black Forest) in August 1965, it was felt that there was a real need for a book on Fourier analysis stressing (i) parallel treatment of Fourier series and Fourier trans forms from a transform point of view, (ii) treatment of Fourier transforms in LP(lRn)_ space not only for p = 1 and p = 2, (iii) classical solution of partial differential equations with completely rigorous proofs, (iv) theory of singular integrals of convolu tion type, (v) applications to approximation theory including saturation theory, (vi) multiplier theory, (vii) Hilbert transforms, Riesz fractional integrals, Bessel potentials, (viii) Fourier transform methods on locally compact groups. This study aims to consider these aspects, presenting a systematic treatment of Fourier analysis on the circle as well as on the infinite line, and of those areas of approximation theory which are in some way or other related thereto. A second volume is in preparation which goes beyond the one-dimensional theory presented here to cover the subject for functions of several variables. Approximately a half of this first volume deals with the theories of Fourier series and of Fourier integrals from a transform point of view.
Elliptic Curves, Modular Forms and Iwasawa Theory
Author: David Loeffler
Publisher: Springer
Published: 2017-01-15
Total Pages: 494
ISBN-13: 3319450328
DOWNLOAD EBOOKCelebrating one of the leading figures in contemporary number theory – John H. Coates – on the occasion of his 70th birthday, this collection of contributions covers a range of topics in number theory, concentrating on the arithmetic of elliptic curves, modular forms, and Galois representations. Several of the contributions in this volume were presented at the conference Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John Coates in Cambridge, March 25-27, 2015. The main unifying theme is Iwasawa theory, a field that John Coates himself has done much to create. This collection is indispensable reading for researchers in Iwasawa theory, and is interesting and valuable for those in many related fields.
Modular Forms
Author: Henri Cohen
Publisher: American Mathematical Soc.
Published: 2017-08-02
Total Pages: 714
ISBN-13: 0821849476
DOWNLOAD EBOOKThe 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.
The Encyclopaedia Britannica: Gichtel-Harmonium
Author:
Publisher:
Published: 1910
Total Pages: 1002
ISBN-13:
DOWNLOAD EBOOK"The last great work of the age of reason, the final instance when all human knowledge could be presented with a single point of view ... Unabashed optimism, and unabashed racism, pervades many entries in the 11th, and provide its defining characteristics ... Despite its occasional ugliness, the reputation of the 11th persists today because of the staggering depth of knowledge contained with its volumes. It is especially strong in its biographical entries. These delve deeply into the history of men and women prominent in their eras who have since been largely forgotten - except by the historians, scholars"-- The Guardian, https://www.theguardian.com/books/booksblog/2012/apr/10/encyclopedia-britannica-11th-edition.
