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Galois Theory and Modular Forms

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ISBN-10: 1402076894

ISBN-13: 9781402076893

Edition: 2004

Authors: Ki-ichiro Hashimoto, Katsuya Miyake, Hiroaki Nakamura

List price: $199.99
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Description:

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. This volume is suitable for advanced undergraduate and graduate students, as well as researchers.
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Book details

List price: $199.99
Copyright year: 2004
Publisher: Springer
Publication date: 11/30/2003
Binding: Hardcover
Pages: 394
Size: 6.50" wide x 9.25" long x 1.25" tall
Weight: 1.782
Language: English

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