On Traces Of Hecke Operators On The Space Of Cusp Forms Of Weight

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On Traces Of Hecke Operators On The Space Of Cusp Forms Of Weight

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Author : Toyokazu Hiramatsu
language : de
Publisher:
Release Date : 1989

On Traces Of Hecke Operators On The Space Of Cusp Forms Of Weight written by Toyokazu Hiramatsu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Cusp forms (Mathematics) categories.

On Traces Of Hecke Operators On The Space Of Cusp Forms Of Weight 1

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Author : T. Hiramatsu
language : en
Publisher:
Release Date : 1989

On Traces Of Hecke Operators On The Space Of Cusp Forms Of Weight 1 written by T. Hiramatsu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Cusp forms (Mathematics) categories.

Traces Of Hecke Operators

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Author : Andrew Knightly
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Traces Of Hecke Operators written by Andrew Knightly 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 2006 with Mathematics categories.

The Fourier coefficients of modular forms are of widespread interest as an important source of arithmetic information. In many cases, these coefficients can be recovered from explicit knowledge of the traces of Hecke operators. The original trace formula for Hecke operators was given by Selberg in 1956. Many improvements were made in subsequent years, notably by Eichler and Hijikata. This book provides a comprehensive modern treatment of the Eichler-Selberg/Hijikata trace formulafor the traces of Hecke operators on spaces of holomorphic cusp forms of weight $\mathtt{k >2$ for congruence subgroups of $\operatorname{SL 2(\mathbf{Z )$. The first half of the text brings together the background from number theory and representation theory required for the computation. Thisincludes detailed discussions of modular forms, Hecke operators, adeles and ideles, structure theory for $\operatorname{GL 2(\mathbf{A )$, strong approximation, integration on locally compact groups, the Poisson summation formula, adelic zeta functions, basic representation theory for locally compact groups, the unitary representations of $\operatorname{GL 2(\mathbf{R )$, and the connection between classical cusp forms and their adelic counterparts on $\operatorname{GL 2(\mathbf{A )$. Thesecond half begins with a full development of the geometric side of the Arthur-Selberg trace formula for the group $\operatorname{GL 2(\mathbf{A )$. This leads to an expression for the trace of a Hecke operator, which is then computed explicitly. The exposition is virtually self-contained, withcomplete references for the occasional use of auxiliary results. The book concludes with several applications of the final formula.

On Traces Of Hecke Operators On The Space Of Cusp Forms Of Weight 1

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Author : T. Hiramatsu
language : en
Publisher:
Release Date : 1989

On Traces Of Hecke Operators On The Space Of Cusp Forms Of Weight 1 written by T. Hiramatsu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Cusp forms (Mathematics) categories.

Modular Forms With Integral And Half Integral Weights

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Author : Xueli Wang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-20

Modular Forms With Integral And Half Integral Weights written by Xueli Wang 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 2013-02-20 with Mathematics categories.

"Modular Forms with Integral and Half-Integral Weights" focuses on the fundamental theory of modular forms of one variable with integral and half-integral weights. The main theme of the book is the theory of Eisenstein series. It is a fundamental problem to construct a basis of the orthogonal complement of the space of cusp forms; as is well known, this space is spanned by Eisenstein series for any weight greater than or equal to 2. The book proves that the conclusion holds true for weight 3/2 by explicitly constructing a basis of the orthogonal complement of the space of cusp forms. The problem for weight 1/2, which was solved by Serre and Stark, will also be discussed in this book. The book provides readers not only basic knowledge on this topic but also a general survey of modern investigation methods of modular forms with integral and half-integral weights. It will be of significant interest to researchers and practitioners in modular forms of mathematics. Dr. Xueli Wang is a Professor at South China Normal University, China. Dingyi Pei is a Professor at Guangzhou University, China.

The Theory Of Jacobi Forms

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Author : Martin Eichler
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-14

The Theory Of Jacobi Forms written by Martin Eichler 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 2013-12-14 with Mathematics categories.

The functions studied in this monogra9h are a cross between elliptic functions and modular forms in one variable. Specifically, we define a Jacobi form on SL (~) to be a holomorphic function 2 (JC = upper half-plane) satisfying the t\-10 transformation eouations 2Tiimcz· k CT +d a-r +b z) (1) ((cT+d) e cp(T, z) cp CT +d ' CT +d (2) rjl(T, z+h+]l) and having a Four·ier expansion of the form 00 e2Tii(nT +rz) (3) cp(T, z) 2: c(n, r) 2:: rE~ n=O 2 r ~ 4nm Here k and m are natural numbers, called the weight and index of rp, respectively. Note that th e function cp (T, 0) is an ordinary modular formofweight k, whileforfixed T thefunction z-+rjl( -r, z) isa function of the type normally used to embed the elliptic curve ~/~T + ~ into a projective space. If m= 0, then cp is independent of z and the definition reduces to the usual notion of modular forms in one variable. We give three other examples of situations where functions satisfying (1)-(3) arise classically: 1. Theta series. Let Q: ~-+ ~ be a positive definite integer valued quadratic form and B the associated bilinear form.

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Author :
language : en
Publisher: World Scientific
Release Date :

written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

The Selberg Trace Formula For Psl 2 R

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Author : Dennis A. Hejhal
language : en
Publisher: Springer
Release Date : 2006-11-15

The Selberg Trace Formula For Psl 2 R written by Dennis A. Hejhal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Codes On Algebraic Curves

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Author : Serguei A. Stepanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Codes On Algebraic Curves written by Serguei A. Stepanov 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 2012-12-06 with Mathematics categories.

This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II). The third is a detailed description of the theory of classical modular curves and their reduction modulo a prime number (Part III). The fourth (and basic) is the construction of geometric Goppa codes and the production of asymptotically good linear codes coming from algebraic curves over finite fields (Part IV). The theory of geometric Goppa codes is a fascinating topic where two extremes meet: the highly abstract and deep theory of algebraic (specifically modular) curves over finite fields and the very concrete problems in the engineering of information transmission. At the present time there are two essentially different ways to produce asymptotically good codes coming from algebraic curves over a finite field with an extremely large number of rational points. The first way, developed by M. A. Tsfasman, S. G. Vladut and Th. Zink [210], is rather difficult and assumes a serious acquaintance with the theory of modular curves and their reduction modulo a prime number. The second way, proposed recently by A.

Arithmetic Geometry Computation And Applications

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Author : Yves Aubry
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-01-11

Arithmetic Geometry Computation And Applications written by Yves Aubry 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 2019-01-11 with Computers categories.

For thirty years, the biennial international conference AGC T (Arithmetic, Geometry, Cryptography, and Coding Theory) has brought researchers to Marseille to build connections between arithmetic geometry and its applications, originally highlighting coding theory but more recently including cryptography and other areas as well. This volume contains the proceedings of the 16th international conference, held from June 19–23, 2017. The papers are original research articles covering a large range of topics, including weight enumerators for codes, function field analogs of the Brauer–Siegel theorem, the computation of cohomological invariants of curves, the trace distributions of algebraic groups, and applications of the computation of zeta functions of curves. Despite the varied topics, the papers share a common thread: the beautiful interplay between abstract theory and explicit results.