Muutke küpsiste eelistusi

E-raamat: Periods And Special Functions In Transcendence

(Texas A&m Univ, Usa)
Teised raamatud teemal:
  • Formaat - EPUB+DRM
  • Hind: 76,05 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Periods And Special Functions In TranscendenceSuurem pilt
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

'The book is mainly addressed to the non-expert reader, in that it assumes only a little background in complex analysis and algebraic geometry, but no previous knowledge in transcendental number theory is required. The technical language is introduced smoothly, and illustrative examples are provided where appropriate The book is carefully written, and the relevant literature is provided in the list of references. 'Mathematical Reviews ClippingsThis book gives an introduction to some central results in transcendental number theory with application to periods and special values of modular and hypergeometric functions. It also includes related results on Calabi-Yau manifolds. Most of the material is based on the author's own research and appears for the first time in book form. It is presented with minimal of technical language and no background in number theory is needed. In addition, except the last chapter, all chapters include exercises suitable for graduate students. It is a nice book for graduate students and researchers interested in transcendence.
Preface vii
Acknowledgments xiii
1 Group Varieties and Transcendence
1(30)
1.1 Group Varieties
2(6)
1.2 Doubly Periodic Functions
8(7)
1.3 Abelian Varieties
15(6)
1.4 Transcendence of Vectors in a Polarized Lattice
21(2)
1.5 Linear Relations between Periods
23(8)
2 Transcendence Results for Exponential and Elliptic Functions
31(24)
2.1 Some Prerequisites from Algebra
32(4)
2.1.1 Size of an Algebraic Integer
32(1)
2.1.2 Siegel's Lemma
33(3)
2.2 Some Prerequisites from Analysis
36(1)
2.3 Transcendence of Values of the Exponential Function
36(8)
2.3.1 Construction of the Auxiliary Function
37(3)
2.3.2 Existence and Choice of a Non-zero F(κ)(μα)
40(1)
2.3.3 Bound F(κ)(μα) from Above Using Zeros of F(z)
41(1)
2.3.4 Bound F(κ)(μα) from Below Using Size Estimate
42(1)
2.3.5 Obtaining a Contradiction
43(1)
2.3.6 Checking the Parameters and Concluding
43(1)
2.4 The Schneider-Lang Theorem and its Corollaries
44(11)
3 Modular Functions and Criteria for Complex Multiplication
55(12)
3.1 The Modular Group PSL(2, Z)
55(3)
3.2 The Elliptic Modular Function
58(3)
3.3 A Transcendence Criterion for CM on Abelian Varieties
61(6)
4 Periods of 1-forms on Complex Curves and Abelian Varieties
67(42)
4.1 The Fundamental Group and the Universal Cover
67(2)
4.2 The First Singular Homology Group
69(3)
4.3 The First de Rham Cohomology Space over R
72(5)
4.4 The First de Rham Cohomology Space over C
77(5)
4.5 Dolbeault Cohomology and Holomorphic 1-Forms
82(2)
4.6 Complex Kahler Manifolds and their First Cohomology
84(3)
4.7 Integrating Forms and the de Rham Theorem
87(2)
4.8 Normalized Periods of Tori and de Rham Cohomology
89(5)
4.9 The Mumford-Tate Group of a Complex Torus
94(4)
4.10 Level 1 Hodge Structures and Transcendence
98(1)
4.11 Algebraic 1-Forms on Riemann Surfaces
99(4)
4.12 Jacobian of a Riemann Surface
103(3)
4.13 Explicit Periods on some Curves with CM
106(3)
5 Transcendence of Special Values of Hypergeometric Functions
109(34)
5.1 Series, Differential Equation, and Euler Integral
109(3)
5.2 Hypergeometric Periods
112(2)
5.3 Monodromy of the Gauss Hypergeometric Function
114(1)
5.4 Deligne-Mostow's Condition INT and Triangle Groups
115(2)
5.5 Arithmetic Triangle Groups
117(4)
5.6 Special Values of Hypergeometric Functions and CM
121(4)
5.7 Exceptional Set and the Edixhoven-Yafaev Theorem
125(3)
5.8 Transcendence Results for Appell-Lauricella Functions
128(12)
5.8.1 Lattice and Arithmeticity Criteria
132(3)
5.8.2 The Exceptional Set and CM
135(3)
5.8.3 Shimura Varieties and Hypergeometric Functions
138(1)
5.8.4 Proof of Theorem 5.5
139(1)
5.9 Ball (n + 3)-tuples and the Exceptional Set
140(3)
6 Transcendence Criterion for Complex Multiplication on K3 Surfaces
143(28)
6.1 Mumford-Tate Group of a Level 2 Hodge Structure
144(3)
6.2 Clifford Algebras
147(1)
6.3 The Kuga-Satake Correspondence
148(3)
6.4 The Kuga-Satake Variety
151(5)
6.5 Transcendence and CM for K3 Hodge Structures
156(1)
6.6 Transcendence Criterion for CM on K3 Surfaces
157(2)
6.7 Kuga-Satake for Hodge Numbers (1, 0, 1)
159(2)
6.8 Examples of Periods on K3 Surfaces
161(10)
7 Hodge Structures of Higher Level
171(28)
7.1 Singular Homology
172(1)
7.2 Hodge Theory of Complex Projective Manifolds
173(2)
7.3 Hodge Filtrations defined over Q and CM
175(9)
7.4 Question 7.2 for Borcea-Voisin Towers
184(8)
7.5 Example of a Viehweg-Zuo Tower
192(4)
7.6 Periods on Fermat Hypersurfaces
196(3)
Bibliography 199(8)
Index 207
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97817863429666e.html
Märksõnad: