On The Theory Of Maass Wave Forms PDF Download
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| Author | : Tobias Mühlenbruch |
| Publisher | : Springer Nature |
| Total Pages | : 527 |
| Release | : 2020-05-06 |
| Genre | : Mathematics |
| ISBN | : 3030404757 |
Download On the Theory of Maass Wave Forms Book in PDF, ePub and Kindle
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.
| Author | : R. Bruggeman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 132 |
| Release | : 2015-08-21 |
| Genre | : Algebraic topology |
| ISBN | : 1470414074 |
Download Period Functions for Maass Wave Forms and Cohomology Book in PDF, ePub and Kindle
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.
| Author | : Masanobu Kaneko |
| Publisher | : World Scientific |
| Total Pages | : 212 |
| Release | : 2015-02-10 |
| Genre | : Mathematics |
| ISBN | : 9814644943 |
Download Number Theory: Plowing and Starring Through High Wave Forms Book in PDF, ePub and Kindle
Based on the successful 7th China–Japan seminar on number theory conducted in Kyushu University, this volume is a compilation of survey and semi-survey type of papers by the participants of the seminar. The topics covered range from traditional analytic number theory to elliptic curves and universality. This volume contains new developments in the field of number theory from recent years and it provides suitable problems for possible new research at a level which is not unattainable. Timely surveys will be beneficial to a new generation of researchers as a source of information and these provide a glimpse at the state-of-the-art affairs in the fields of their research interests. Contents:On Modular Relations (Tomihiro Arai, Kalyan Chakraborty and Shigeru Kanemitsu)Figurate Primes and Hilbert's 8th Problem (Tianxin Cai, Yong Zhang and Zhongyan Shen)Statistical Distribution of Roots of a Polynomial Modulo Prime Powers (Yoshiyuki Kitaoka)A Survey on the Theory of Universality for Zeta and L-Functions (Kohji Matsumoto)Complex Multiplication in the Sense of Abel (Katsuya Miyake)Problems on Combinatorial Properties of Primes (Zhi-Wei Sun) Readership: Graduate students and researchers in number theory. Key Features:Includes some new topics of interest to complement the previous three volumes in the books seriesContains well-written and informative surveys in several fields in number theoryEach paper contains some new problems for research which a beginner researcher can try onAs a tradition, the editors devoted efforts to make the volume as readable as possibleKeywords:Analytic Number Theory;Ellipic Curves;Universality;Figurate Primes;Zeta Functions;Modular Relations;L-Functions
| Author | : Dennis A. Hejhal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 693 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461215447 |
Download Emerging Applications of Number Theory Book in PDF, ePub and Kindle
Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.
| Author | : M. Ram Murty |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 188 |
| Release | : 2012-10-05 |
| Genre | : Mathematics |
| ISBN | : 813220770X |
Download The Mathematical Legacy of Srinivasa Ramanujan Book in PDF, ePub and Kindle
Srinivasa Ramanujan was a mathematician brilliant beyond comparison who inspired many great mathematicians. There is extensive literature available on the work of Ramanujan. But what is missing in the literature is an analysis that would place his mathematics in context and interpret it in terms of modern developments. The 12 lectures by Hardy, delivered in 1936, served this purpose at the time they were given. This book presents Ramanujan’s essential mathematical contributions and gives an informal account of some of the major developments that emanated from his work in the 20th and 21st centuries. It contends that his work still has an impact on many different fields of mathematical research. This book examines some of these themes in the landscape of 21st-century mathematics. These essays, based on the lectures given by the authors focus on a subset of Ramanujan’s significant papers and show how these papers shaped the course of modern mathematics.
| Author | : Henri Cohen |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 700 |
| Release | : 2017-08-02 |
| Genre | : Forms (Mathematics). |
| ISBN | : 0821849476 |
Download Modular Forms: A Classical Approach Book in PDF, ePub and Kindle
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.
| Author | : Michel Laurent Lapidus |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 210 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 0821820796 |
Download Dynamical, Spectral, and Arithmetic Zeta Functions Book in PDF, ePub and Kindle
The original zeta function was studied by Riemann as part of his investigation of the distribution of prime numbers. Other sorts of zeta functions were defined for number-theoretic purposes, such as the study of primes in arithmetic progressions. This led to the development of $L$-functions, which now have several guises. It eventually became clear that the basic construction used for number-theoretic zeta functions can also be used in other settings, such as dynamics, geometry, and spectral theory, with remarkable results. This volume grew out of the special session on dynamical, spectral, and arithmetic zeta functions held at the annual meeting of the American Mathematical Society in San Antonio, but also includes four articles that were invited to be part of the collection. The purpose of the meeting was to bring together leading researchers, to find links and analogies between their fields, and to explore new methods. The papers discuss dynamical systems, spectral geometry on hyperbolic manifolds, trace formulas in geometry and in arithmetic, as well as computational work on the Riemann zeta function. Each article employs techniques of zeta functions. The book unifies the application of these techniques in spectral geometry, fractal geometry, and number theory. It is a comprehensive volume, offering up-to-date research. It should be useful to both graduate students and confirmed researchers.
| Author | : Jens Bölte |
| Publisher | : Cambridge University Press |
| Total Pages | : 285 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 1107610494 |
Download Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology Book in PDF, ePub and Kindle
Leading experts introduce this classical subject with exciting new applications in theoretical physics.
| Author | : Roelof Bruggeman |
| Publisher | : American Mathematical Society |
| Total Pages | : 186 |
| Release | : 2023-07-31 |
| Genre | : Mathematics |
| ISBN | : 1470465450 |
Download Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume Book in PDF, ePub and Kindle
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| Author | : George E. Andrews |
| Publisher | : Springer |
| Total Pages | : 736 |
| Release | : 2018-02-01 |
| Genre | : Mathematics |
| ISBN | : 3319683764 |
Download Analytic Number Theory, Modular Forms and q-Hypergeometric Series Book in PDF, ePub and Kindle
Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory. Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.
