Galois Theory and Modular Forms / Edition 1

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Overview

The key words for the book are "Galois groups", or more precisely "generic polynomials","Galois coverings of algebraic curves" and "Shimura varieties". The work includes surveys on branches of research areas and many articles, all critically refereed by experts, which present the latest research results with carefully written expository introductions. The topics cover a wide range which nonetheless have a common thread.

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Product Details

  • ISBN-13: 9781402076893
  • Publisher: Springer US
  • Publication date: 11/30/2003
  • Series: Developments in Mathematics Series, #11
  • Edition description: 2003
  • Edition number: 1
  • Pages: 394
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.94 (d)

Table of Contents

Preface
The arithmetic of Weierstrass points on modular curves X[subscript 0](p) 3
Semistable abelian varieties with small division fields 13
Q-curves with rational j-invariants and jacobian surfaces of GL[subscript 2]-type 39
Points defined over cyclic quartic extensions on an elliptic curve and generalized Kummer surfaces 65
The absolute anabelian geometry of hyperbolic curves 77
Regular Galois realizations of PSL[subscript 2](p[subscript 2]) over Q(T) 125
Middle convolution and Galois realizations 143
On the essential dimension of p-groups 159
Explicit constructions of generic polynomials for some elementary groups 173
On dihedral extensions and Frobenius extensions 195
On the non-existence of certain Galois extensions 221
Frobenius modules and Galois groups 233
On quadratic number fields each having an unramified extension which properly contains the Hilbert class field of its genus field 271
Distribution of units of an algebraic number field 287
On capitulation problem for 3-manifolds 305
On the Iwasawa [mu]-invariant of the cyclotomic Z[subscript p]-extension of certain quartic fields 315
Quasimodular solutions of a differential equation of hypergeometric type 329
Special values of the standard zeta functions 337
p-adic properties of values of the modular j-function 357
Thompson series and Ramanujan's identities 367
Generalized Rademacher functions and some congruence properties 375
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