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Introduction to Modular Forms 1st ed. 1976. Corr. 3rd printing 2001 [Hardback]

  • Formāts: Hardback, 265 pages, height x width: 235x155 mm, weight: 1260 g, IX, 265 p., 1 Hardback
  • Sērija : Grundlehren der mathematischen Wissenschaften 222
  • Izdošanas datums: 01-Dec-1976
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540078339
  • ISBN-13: 9783540078333
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Introduction to Modular Forms 1st ed. 1976. Corr. 3rd printing 2001Palielināt
  • Formāts: Hardback, 265 pages, height x width: 235x155 mm, weight: 1260 g, IX, 265 p., 1 Hardback
  • Sērija : Grundlehren der mathematischen Wissenschaften 222
  • Izdošanas datums: 01-Dec-1976
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540078339
  • ISBN-13: 9783540078333
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783540078333.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#

Part I. Classical Theory 3(54)
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 XXX\XXX(*) 24(5)
2. Congruence Subgroups 29(3)
3. Differential Forms and Modular Forms 32(3)
4. The Petersson Scalar Product 35(9) Appendix The Eichler-Selberg Trace Formula on SL(2)(Z) 44(13) D. Zagier Part II. Periods of Cusp Forms 57(44)
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 SL(2)(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 SL(2)(Z) 84(17)
1. The Polynomial Representation 85(3)
2. The Shimura Product on Differential 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 101(50)
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 151(56)
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 is greater than equal to 5 164(5)
8. The Operation of XXX on M 169(7)
Chapter XI. Galois Representations 176(31)
1. Simplicity 177(3)
2. Subgroups of GL(2) 180(7)
3. Applications to Congruences of the Trace of Frobenius 187(11) Appendix Exceptional Subgroups of GL(2) 198(9) Walter Feit Part V. p-Adic Distributions 207(48)
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 Z(p)((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