Proceedings of the Saga-TMU conferences on "Galois Theory and Modular Forms"

Galois Theory and Modular Forms

Kluwer Academic Publishers

Springer Link

Copyright : 2001 Kluwer Academic Publishers.
Kluwer Academic Publishers, Boston
Hardbound, ISBN 1-4020-7689-4
October 2003, 406 pp.

edited by
Ki-ichiro Hashimoto
Dept. of Science and Technology, Waseda University, Tokyo, Japan
Katsuya Miyake
Dept. of Mathematics, Tokyo Metropolitan University, Japan
Hiroaki Nakamura
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 common thread.
This volume is suitable for advanced undergraduate and graduate students, as well as researchers.
Table of Contents

Preface [pdf]

Part 1: Arithmetic geometry
Scott Ahlgren "The arithmetic of Weierstrass points on modular curves X_0(p)"
Armand Brumer and Kenneth Kramer "Semistable abelian varieties with small division fields"
Kiichiro Hashimoto "Q-curves with rational j-invariants and jacobian surfaces of GL2-type"
Masato Kuwata "Points defined over cyclic quartic extensions on an elliptic curve and generalized Kummer surfaces"
Shinichi Mochizuki "The absolute anabelian geometry of hyperbolic curves"

Part 2: Galois groups and Galois extensions
Takehito Shiina "Regular Galois realizations of PSL_2(p^2) over Q(T)"
Michael Dettweiler "Middle convolution and Galois realizations"
Arne Ledet "On the essential dimension of p-groups"
Yuichi Rikuna "Explicit constructions of generic polynomials for some elementary groups"
Yasuhiro Kishi and Masafumi Imaoka "On dihedral extensions and Frobenius extensions"
Hyunsuk Moon "On the non-existence of certain Galois extensions"
Bernd Heinrich Matzat "Frobenius modules and Galois groups"

Part 3: Algebraic number theory
Ken Yamamura "On quadratic number fields each having an unramified extension which properly contains the Hilbert class field of its genus field "
Yoshiyuki Kitaoka "Distribution of units of an algebraic number field"
Masanori Morishita "On capitulation problem for 3-manifolds"
Tsuyoshi Itoh "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"
Hidenori Katsurada "Special values of the standard zeta functions"
Ken Ono and Mattew A. Papanikolas "p-adic properties of values of the modular j-functions"
Masao Koike "Thompson series and Ramanujan's identities"
Hiroaki Nakamura "Generalized Rademacher functions and some congruence properties"

Workshop informations