دانلود کتاب Complex multiplication

عنوان فارسی :

دانلود کتاب ضرب پیچیده

عنوان انگلیسی :

Complex multiplication

زبان : English

موضوع : Mathematics->Number Theory

نویسندگان : Reinhard Schertz

ناشر : CUP

ISBN (شابک) : 9780521766685, 0521766680

تعداد صفحات : 377\377

سال نشر : 2010     ویرایش :

حجم : 2 MB       فرمت : pdf

قیمت : 20000 تومان

فهرست :



Table of contents :
Contents......Page 9
Preface......Page 13
1.1 Values of elliptic functions......Page 17
1.2 The functions…......Page 19
1.3 Construction of elliptic functions......Page 23
1.4 Algebraic and geometric properties of elliptic functions......Page 25
1.5 Division polynomials......Page 29
1.6 Weierstrass functions......Page 32
1.6.1 Expansions at zero......Page 34
1.6.2 p-adic limits......Page 39
1.7 Elliptic resolvents......Page 43
1.8 q-expansions......Page 48
1.9 Dedekind's eta function and sigma-product formula......Page 51
1.10 The transformation formula of the Dedekind eta function......Page 54
2 Modular functions......Page 57
2.1 The modular group......Page 58
2.2 Congruence subgroups......Page 61
2.3 Definition of modular forms......Page 64
2.4.2 The functions…......Page 66
2.4.3 eta-quotients......Page 67
2.4.4 Weber's tau function......Page 68
2.4.7 Transformation of…......Page 69
2.5.1 Construction of modular functions for Gamma......Page 70
2.5.2 The q-expansion principle......Page 75
2.6.1 The isomorphisms of CU/CGamma......Page 77
2.6.2 The extended q-expansion principle......Page 78
2.7 Modular functions for GammaR......Page 79
2.8 Modular functions for Gamma(N)......Page 85
2.9 The field Q(gamma2, gamma3)......Page 88
2.10 Lower powers of eta-quotients......Page 90
3.1.1 Fractional ideals, integral ideals, proper ideals, regular ideals......Page 98
3.1.2 Ideal groups......Page 102
3.1.3 Primitive matrices and bases of ideals......Page 110
3.1.4 Integral ideals that are not regular......Page 114
3.2 Density theorems......Page 116
3.3 Class field theory......Page 119
4.1 Singular values......Page 127
4.2 Factorisation of varphi A (alpha)......Page 130
4.3 Factorisation of…......Page 134
4.4 A result of Dorman, Gross and Zagier......Page 137
5.1 The Reciprocity Law of Weber, Hasse, Söhngen, Shimura......Page 138
5.2 Applications of the Reciprocity Law......Page 144
6.1 Generation of ring class fields by singular values of j......Page 154
6.2 Generation of ray class fields by tau and j......Page 157
6.3 The singular values of gamma 2 and gamma 3......Page 160
6.4 The singular values of Schläfli's functions......Page 164
6.5 Heegner's solution of the class number one problem......Page 167
6.6 Generation of ring class fields by eta-quotients......Page 170
6.7 Double eta-quotients in the ramified case......Page 181
6.8 Generation of ray class fields by…......Page 185
6.9 Generalised principal ideal theorem......Page 199
7 Integral basis in ray class fields......Page 206
7.1 A normalisation of the Weierstrass…......Page 207
7.2 The discriminant of…......Page 209
7.3 The denominator of…......Page 213
7.4 Construction of relative integral basis......Page 217
7.4.1 Analogy to cyclotomic fields......Page 219
7.5 Relative integral power basis......Page 221
7.6 Bley's generalisation for…......Page 226
8 Galois module structure......Page 229
8.1 Torsion points and good reduction......Page 230
8.2 Kummer theory of E......Page 231
8.3 Integral objects......Page 233
8.4 Global construction of…......Page 236
8.5 Construction of a generating element for…......Page 237
8.6 Galois module structure of ray class fields......Page 240
8.7.1 The Weierstrass model......Page 244
8.7.2 The Fueter model......Page 245
8.7.3 The Deuring model......Page 247
8.7.4 Singular values of the Weierstrass, Fueter and Deuring functions......Page 248
8.7.5 Singular values of Weierstrass functions......Page 250
8.8 Proofs of Theorems 8.3.1 and 8.5.1......Page 254
8.9 Proofs of Theorems 8.4.1, 8.4.2 and 8.5.2......Page 261
8.10 Proofs of Theorems 8.9.2 and 8.6.2......Page 266
8.11 Analogy to the cyclotomic case......Page 269
8.12 Generalisation to ring classes by Bettner and Bley......Page 272
9.1 Bettner's results......Page 277
9.2 Method of proof......Page 279
10.1 Reduction of the Weierstrass model......Page 282
10.2 Computation of…......Page 289
10.2.1 Schläfli–Weber functions......Page 291
10.2.2 Double eta-quotients......Page 292
10.2.3 Application of eta-quotients in the ramified case......Page 294
10.3.1 Reduction of the Fueter model......Page 298
10.3.2 Reduction of the Deuring model......Page 301
11 The class number formulae of Curt Meyer......Page 304
11.1 L-Functions of ring class characters......Page 305
11.2 L-function s of ray class characters…......Page 307
11.3 Class number formulae......Page 309
12.1 Group-theoretical lemmas for the case…......Page 311
12.2 Applications of Theorems 12.1.1, 12.1.2......Page 317
12.2.1 Application of Theorem 12.1.1......Page 318
12.2.2 Application of Theorem 12.1.2......Page 319
12.3 Class number formulae for…......Page 320
12.4 Class number formulae for…......Page 325
12.4.1.1 Divisibility between class numbers......Page 333
12.4.1.2 Divisibility of class numbers by divisors of the field degree......Page 338
12.5 Group-theoretical lemmas for…......Page 339
12.6 The Galois group of MK/K......Page 352
12.7 Class number formulae for…......Page 354
12.8 Class number formulae for…......Page 357
12.8.1.1 Divisibility relations between class numbers......Page 362
12.8.1.2 Divisibility of class numbers by divisors of the field degree......Page 364
References......Page 367
Index of Notation......Page 372
Index......Page 376





کتاب های پزشکی

دانلود کتاب Pharmaceutical Sales Force Strategies

دانلود کتاب Essentials of Medical Genomics

دانلود کتاب Clinical Malignant Hematology

دانلود کتاب Yamada's Textbook of Gastroenterology

دانلود کتاب Physio-medical therapeutics, materia medica, and pharmacy.

کتاب های کامپیوتر

دانلود کتاب Psychology of Computer Programming

دانلود کتاب MATLAB Programming for Engineers B01_0562

دانلود کتاب Data mining in biomedicine using ontologies

دانلود کتاب Programming Erlang: Software for a Concurrent World

دانلود کتاب Killer Game Programming in Java

کتاب های ریاضی

دانلود کتاب Lectures on the many-electron problem (Interscience monographs and texts in physics and astronomy)

دانلود کتاب Integration of Equations of Parabolic Type By the Method of Nets; International Series of Monographs on Pure and Applied Mathematics Volume 54

دانلود کتاب Lie Groups and Lie Algebras II

دانلود کتاب Nonlinear dispersive equations: Local and global analysis

دانلود کتاب Direct and indirect boundary integral equation methods

کتاب های تکنولوژی

دانلود کتاب Stainless Steels. Their properties and their suitability for welding

دانلود کتاب Particulate Systems in Nano- and Biotechnologies

دانلود کتاب Hormones and Reproduction of Vertebrates - Volume 5: Mammals

دانلود کتاب Low-Power Variation-Tolerant Design in Nanometer Silicon

دانلود کتاب Protein Nanotechnology: Protocols, Instrumentation, and Applications (Methods in Molecular Biology)

کتاب های مذهبی

دانلود کتاب Noah's Curse: The Biblical Justification of American Slavery

دانلود کتاب Show Them No Mercy: 4 Views on God and Canaanite Genocide

دانلود کتاب A Charmed Life

دانلود کتاب The Doctrine of Vibration: An Analysis of the Doctrines and Practices of Kashmir Shaivism

دانلود کتاب The Death of Christian Culture

کتاب های فیزیولوژی

دانلود کتاب Pedagogy, Oppression and Transformation in a 'Post-Critical' Climate: The Return to Freirean Thinking

دانلود کتاب Sexopedia

دانلود کتاب Language Play, Language Learning (Oxford Applied Linguistics)

دانلود کتاب Abnormal Psychology (International Library of Psychology)

دانلود کتاب Global Promise: Quality Assurance and Accountability in Professional Psychology

کتاب های تاریخی

دانلود کتاب This House of Noble Deeds

دانلود کتاب British Territorial Units 1914-18

دانلود کتاب Sepecat Jaguar In Action

دانلود کتاب Spanish Army of the Napoleonic Wars (2): 1808-12

دانلود کتاب Stuka Volume One: Luftwaffe Ju 87 Dive-Bomber Units 1939-1941 (Luftwaffe Colours)

کتاب های زیست شناسی

دانلود کتاب Receptor Binding Techniques

دانلود کتاب Plant amino acids. Biochemistry and biotechnology

دانلود کتاب Yac Protocols

دانلود کتاب Curious Creatures in Zoology

دانلود کتاب Biosensors and Biodetection

کتاب های اقتصاد

دانلود کتاب The Economist - 20 January 2001

دانلود کتاب PMP Project Management Professional Study Guide

دانلود کتاب Managing Archaeology

دانلود کتاب Supply Chain Risk Management: Vulnerability and Resilience in Logistics

دانلود کتاب Reconstructing Project Management

کتاب های آموزشی

دانلود کتاب Color Management for Digital Photographers For Dummies

دانلود کتاب Brands That Rock What Business Leaders Can Learn from the World of Rock and Roll

دانلود کتاب Complete idiots guide to Jogging & Running

دانلود کتاب Judgment and Planning in Chess

دانلود کتاب Digital Frequency Synthesis Demystified

کتاب های حقوق

دانلود کتاب Direct and Indirect Characteristic X-Rays Their Ratio as a Function of Cathode-Ray Energy

دانلود کتاب Law Antisemitism and the Holocaust (Glasshouse)

دانلود کتاب How America Gets Away With Murder: Illegal Wars, Collateral Damage and Crimes Against Humanity

دانلود کتاب Inside Gitmo: The True Story Behind the Myths of Guantanamo Bay

دانلود کتاب Cultivating Conscience: How Good Laws Make Good People

کتاب های علوم انسانی

دانلود کتاب The environment: its role in psychosocial functioning and psychotherapy

دانلود کتاب The Philosopher in Plato's Statesman

دانلود کتاب A Concise Encyclopedia of the United Nations, 2nd Edition

دانلود کتاب There is no death

دانلود کتاب Cyberpop: digital lifestyles and commodity culture