Proceedings of the Saga-TMU conferences on
"Galois Theory and Modular Forms"
Galois Theory and Modular Forms
DEVELOPMENTS IN MATHEMATICS : Volume 11
Kluwer Academic Publishers
Copyright : 2001
Kluwer Academic Publishers.
Kluwer Academic Publishers, Boston
Hardbound, ISBN 1-4020-7689-4
October 2003, 406 pp.
Dept. of Science and Technology, Waseda University, Tokyo, Japan
Dept. of Mathematics, Tokyo Metropolitan University, Japan
Dept. of Mathematics, Okayama University, Japan
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
This volume is suitable for advanced undergraduate and
graduate students, as well as researchers.
Table of Contents
Part 1: Arithmetic geometry
"The arithmetic of Weierstrass points on modular curves X_0(p)"
Armand Brumer and Kenneth Kramer
"Semistable abelian varieties with small division fields"
"Q-curves with rational j-invariants and jacobian
surfaces of GL2-type"
"Points defined over cyclic quartic extensions on an elliptic curve
and generalized Kummer surfaces"
"The absolute anabelian geometry of hyperbolic curves"
Part 2: Galois groups and Galois extensions
"Regular Galois realizations of PSL_2(p^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"
Yasuhiro Kishi and Masafumi Imaoka
"On dihedral extensions and Frobenius extensions"
"On the non-existence of certain Galois extensions"
Bernd Heinrich Matzat
"Frobenius modules and Galois groups"
Part 3: 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 cyclotomoic Z_p-extension of
certain quartic fields"
Part 4: Modular forms and arithmetic functions
Masanobu Kaneko and Masao Koike
"Quasimodular solutions of a differential equation
of hypergeometric type"
"Special values of the standard zeta functions"
Ken Ono and Mattew A. Papanikolas
"p-adic properties of values of the modular j-functions"
"Thompson series and Ramanujan's identities"
"Generalized Rademacher functions and
some congruence properties"