Galois Theory and Modular Forms

Name: Galois Theory and Modular Forms
Price: 169.17 USD
Availability: InStock
ISBN: 9781402076893

ISBN-10: 1402076894

ISBN-13: 9781402076893

Edition: 2004

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

List price: $169.99

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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.

Book details

List price: $169.99
Copyright year: 2004
Publisher: Springer
Publication date: 11/30/2003
Binding: Hardcover
Pages: 394
Size: 6.10" wide x 9.25" long x 1.25" tall
Weight: 3.630
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