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Introduction to Modular Forms Softcover reprint of the original 1st ed. 1987 [Mīkstie vāki]

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  • Formāts: Paperback / softback, 265 pages, height x width: 235x155 mm, weight: 454 g, IX, 265 p., 1 Paperback / softback
  • Sērija : Grundlehren der mathematischen Wissenschaften 222
  • Izdošanas datums: 19-Oct-2010
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642057160
  • ISBN-13: 9783642057168
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Introduction to Modular Forms Softcover reprint of the original 1st ed. 1987Palielināt
  • Formāts: Paperback / softback, 265 pages, height x width: 235x155 mm, weight: 454 g, IX, 265 p., 1 Paperback / softback
  • Sērija : Grundlehren der mathematischen Wissenschaften 222
  • Izdošanas datums: 19-Oct-2010
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642057160
  • ISBN-13: 9783642057168
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783642057168.html
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From the reviews: "This book gives a thorough introduction to several theories that are fundamental to research on modular forms. Most of the material, despite its importance, had previously been unavailable in textbook form. Complete and readable proofs are given... In conclusion, this book is a welcome addition to the literature for the growing number of students and mathematicians in other fields who want to understand the recent developments in the theory of modular forms." #Mathematical Reviews# "This book will certainly be indispensable to all those wishing to get an up-to-date initiation to the theory of modular forms." #Publicationes Mathematicae#

Recenzijas

From the reviews: "This book gives a thorough introduction to several theories that are fundamental to research on modular forms. Most of the material, despite its importance, had previously been unavailable in textbook form. Complete and readable proofs are given... In conclusion, this book is a welcome addition to the literature for the growing number of students and mathematicians in other fields who want to understand the recent developments in the theory of modular forms." #Mathematical Reviews# "This book will certainly be indispensable to all those wishing to get an up-to-date initiation to the theory of modular forms." #Publicationes Mathematicae#

Papildus informācija

Springer Book Archives
Part I Classical Theory
Chapter I Modular Forms
3(13)
§1 The Modular Group
3(2)
§ 2 Modular Forms
5(7)
§ 3 The Modular Function j
12(1)
§ 4 Estimates for Cusp Forms
12(2)
§ 5 The Mellin Transform
14(2)
Chapter II Hecke Operators
16(8)
§ 1 Definitions and Basic Relations
16(5)
§ 2 Euler Products
21(3)
Chapter III Petersson Scalar Product
24(33)
§ 1 The Riemann Surface
24(5)
§ 2 Congruence Subgroups
29(3)
§ 3 Differential Forms and Modular Forms
32(3)
§ 4 The Petersson Scalar Product
35(22)
Appendix by D. Zagier. The Eichler--Selberg Trace Formula on SL2(Z)
44(13)
Part II Periods of Cusp Forms
Chapter IV Modular Symbols
57(11)
§ 1 Basic Properties
57(4)
§ 2 The Manin-Drinfeld Theorem
61(4)
§ 3 Hecke Operators and Distributions
65(3)
Chapter V Coefficients and Periods of Cusp Forms on SL2(Z)
68(16)
§ 1 The Periods and Their Integral Relations
69(4)
§ 2 The Manin Relations
73(3)
§ 3 Action of the Hecke Operators on the Periods
76(5)
§ 4 The Homogeneity Theorem
81(3)
Chapter VI The Eichler--Shimura Isomorphism on SL2(Z)
84(17)
§ 1 The Polynomial Representation
85(3)
§ 2 The Shimura Product on Differentia! Forms
88(1)
§ 3 The Image of the Period Mapping
89(4)
§ 4 Computation of Dimensions
93(3)
§ 5 The Map into Cohomology
96(5)
Part III Modular Forms for Congruence Subgroups
Chapter VII Higher Levels
101(17)
§ 1 The Modular Set and Modular Forms
101(4)
§ 2 Hecke Operators
105(3)
§ 3 Hecke Operators on q-Expansions
108(3)
§ 4 The Matrix Operation
111(1)
§ 5 Petersson Product
112(2)
§ 6 The Involution
114(4)
Chapter VIII Atkin--Lehner Theory
118(20)
§ 1 Changing Levels
118(4)
§ 2 Characterization of Primitive Forms
122(1)
§ 3 The Structure Theorem
123(3)
§ 4 Proof of the Main Theorem
126(12)
Chapter IX The Dedekind Formalism
138(13)
§ 1 The Transformation Formalism
138(4)
§ 2 Evaluation of the Dedekind Symbol
142(9)
Part IV Congruence Properties and Galois Representations
Chapter X Congruences and Reduction mod p
151(25)
§ 1 Kummer Congruences
151(2)
§ 2 Von Staudt Congruences
153(1)
§ 3 q-Expansions
154(2)
§ 4 Modular Forms over Z[ 1/2, 1/3]
156(3)
§ 5 Derivatives of Modular Forms
159(3)
§ 6 Reduction mod p
162(2)
§ 7 Modular Forms mod p, p ≥ 5
164(5)
§ 8 The Operation of θ on M
169(7)
Chapter XI Galois Representations
176(31)
§ 1 Simplicity
177(3)
§ 2 Subgroups of GL2
180(7)
§ 3 Applications to Congruences of the Trace of Frobenius
187(20)
Appendix by Walter Feit. Exceptional Subgroups of GL2
198(9)
Part V p-Adic Distributions
Chapter XII General Distributions
207(21)
§ 1 Definitions
207(3)
§ 2 Averaging Operators
210(7)
§ 3 The Iwasawa Algebra
217(2)
§ 4 Weierstrass Preparation Theorem
219(2)
§ 5 Modules over Zp[ [ T]]
221(7)
Chapter XIII Bernoulli Numbers and Polynomials
228(12)
§ 1 Bernoulli Numbers and Polynomials
228(5)
§ 2 The Integral Distribution
233(3)
§ 3 L-Functions and Bernoulli Numbers
236(4)
Chapter XIV The Complex L-Functions
240(7)
§ 1 The Hurwitz Zeta Function
240(4)
§ 2 Functional Equation
244(3)
Chapter XV The Hecke--Eisenstein and Klein Forms
247(8)
§ 1 Forms of Weight 1
247(4)
§ 2 The Klein Forms
251(1)
§ 3 Forms of Weight 2
252(3)
Bibliography 255(5)
Subject Index 260