On Congruence Monodromy Problems

Author(s) Yasutaka Ihara

MSJ Memoirs, 18: 230pp. (2008). DOI: 10.2969/msjmemoirs/018010000

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This book consists of two parts: a reproduction of the author's unpublished Lecture Notes (1968-69), and his Author's Notes (2008). The former starts with three main conjectural relationships and gives various approaches towards their proofs. Though they remained formally unpublished, these Lecture Notes circulated widely and have stimulated research in various directions. The main conjectures themselves have been proved since then. The Author's Notes (2008) give detailed explanations of these developments, together with open problems.

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Mathematical Society of Japan Memoirs, Volume 18

230 pp.

Published: 2008

First available in Project Euclid: 25 November 2014

zbMATH: 1166.14301

MathSciNet: MR2499876

Digital Object Identifier: 10.2969/msjmemoirs/018010000

ISBN: 9784931469501

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Title and Copyright Pages

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, i-vi (2008). Open Access

Contents

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, vii-ix (2008). Open Access

Preface to Volume 1

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, xi-xi (2008). Open Access

Preface to Volume 2

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, xiii-xiii (2008). Open Access

General Introduction

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, xv-xvi (2008). Open Access

Notations

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, xvii-xvii (2008). Open Access

Chapter 1. Part 1. The group $\Gamma$ and its $\zeta$-function

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, 1-27 (2008). https://doi.org/10.2969/msjmemoirs/01801C01-10 Open Access

Chapter 1. Part 2. Detailed study of elements of $\Gamma$ with parabolic and elliptic real parts; the general formula for $\zeta_{\Gamma}(u)$

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, 28-61 (2008). https://doi.org/10.2969/msjmemoirs/01801C01-20 Open Access

Chapter 2. Introduction to Part 1 and Part 2

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, 63-64 (2008). https://doi.org/10.2969/msjmemoirs/01801C020 Open Access

Chapter 2. Part 1. The $G_{\mathfrak p}$-fields over $\mathbf{C}$

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, 65-82 (2008). https://doi.org/10.2969/msjmemoirs/01801C02-10 Open Access

Chapter 2. Part 2. Full $G_{\mathfrak p}$-subfields over algebraic number fields

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, 83-105 (2008). https://doi.org/10.2969/msjmemoirs/01801C02-20 Open Access

Chapter 2. Introduction to Part 3A and Part 3B

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, 106-108 (2008). https://doi.org/10.2969/msjmemoirs/01801C02-30 Open Access

Chapter 2. Part 3A. The canonical $S$-operator and the canonical class of linear differential equations of second order on algebraic function field $L$ of one variable over $\mathbf{C}$, and their algebraic characterizations when $L$ is "arithmetic"

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, 109-125 (2008). https://doi.org/10.2969/msjmemoirs/01801C02-3A0 Open Access

Chapter 2. Part 3B. Unique existence of an invariant $S$-operator on "arithmetic" algebraic function fields (including $G_{\mathfrak p}$-fields) over any field of characteristic zero

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, 126-135 (2008). https://doi.org/10.2969/msjmemoirs/01801C02-3B0 Open Access

Chapter 3. Part 1. Some properties of $\Gamma$

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, 137-152 (2008). https://doi.org/10.2969/msjmemoirs/01801C03-10 Open Access

Chapter 4. Part 1. Examples of $\Gamma$

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, 153-157 (2008). https://doi.org/10.2969/msjmemoirs/01801C04-10 Open Access

Chapter 5. Part 1. Elliptic modular functions mod $p$ and $\Gamma = PSL_{2}(\mathbf{Z}^{(p)})$

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, 159-167 (2008). https://doi.org/10.2969/msjmemoirs/01801C05-10 Open Access

Chapter 5. Part 2. Non-abelian classfields attached to subgroups of $\Gamma = PSL_{2}(\mathbf{Z}^{(p)})$ with finite indices

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, 168-206 (2008). https://doi.org/10.2969/msjmemoirs/01801C05-20 Open Access

Supplements

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, 207-214 (2008). https://doi.org/10.2969/msjmemoirs/01801C060 Open Access

Bibliography

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, 215-216 (2008). Open Access

Author's Notes (2008)

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, 217-228 (2008). https://doi.org/10.2969/msjmemoirs/01801C070 Open Access

Additional References

Yasutaka Ihara

Mathematical Society of Japan Memoirs Vol. 18, 229-230 (2008). Open Access

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