Elliptic and Modular Functions from Gauss to Dedekind to HeckeCambridge University Press, 18 d’abr. 2017 - 475 pàgines This thorough work presents the fundamental results of modular function theory as developed during the nineteenth and early-twentieth centuries. It features beautiful formulas and derives them using skillful and ingenious manipulations, especially classical methods often overlooked today. Starting with the work of Gauss, Abel, and Jacobi, the book then discusses the attempt by Dedekind to construct a theory of modular functions independent of elliptic functions. The latter part of the book explains how Hurwitz completed this task and includes one of Hurwitz's landmark papers, translated by the author, and delves into the work of Ramanujan, Mordell, and Hecke. For graduate students and experts in modular forms, this book demonstrates the relevance of these original sources and thereby provides the reader with new insights into contemporary work in this area. |
Continguts
The Basic Modular Forms of the Nineteenth Century | 1 |
Hermites Transformation of Theta Functions | 5 |
Gausss Contributions to Modular Forms | 13 |
Abel and Jacobi on Elliptic Functions | 42 |
5 | 132 |
6 | 149 |
7 | 188 |
8 | 212 |
The Theory of Modular Forms as Reworked by Hurwitz | 334 |
Ramanujans Euler Products and Modular Forms | 344 |
Dirichlet Series and Modular Forms | 371 |
Sums of Squares | 384 |
The Hecke Operators | 426 |
Translation of Hurwitzs Paper of 1904 | 445 |
| 463 | |
| 471 | |
Altres edicions - Mostra-ho tot
Elliptic and Modular Functions from Gauss to Dedekind to Hecke Ranjan Roy Previsualització limitada - 2017 |
Frases i termes més freqüents
Abel algebraic applied called Chapter coefficients complex connection considered constant contained convergent corresponding cusp Dedekind defined denoted derive determine differential Dirichlet series divisors Eisenstein elliptic functions employed equation equivalent example exist expansion expressed fact factor follows formula four fundamental Gauss gave given gives Glaisher half-plane Hecke hence Hermite Hurwitz identity implies independent infinite integer invariant Jacobi Klein later lectures mathematics matrix means method modular equation modular forms modular functions Mordell multiplier Note number of representations Observe obtain particular periods polynomial positive powers presented prime problem proof proved published quadratic Ramanujan Recall region relation remark respectively result Riemann roots satisfied showed side signature similar solutions squares theorem theory transformation values write written wrote zero