An introduction to non-Abelian class field theory : automorphic forms of weight 1 and 2-dimensional Galois representations

書誌事項

An introduction to non-Abelian class field theory : automorphic forms of weight 1 and 2-dimensional Galois representations

Toyokazu Hiramatsu, Seiken Saito

(Series on number theory and its applications / series editor, Shigeru Kanemitsu, v. 13)

World Scientific, c2017

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注記

Includes bibliographical references (p. 165-171) and index

内容説明・目次

内容説明

This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations. One of the outstanding problems in arithmetic is a generalization of class field theory to non-abelian Galois extension of number fields. In this volume, we discuss some relations between this problem and cusp forms of weight 1.

目次

  • Higher Reciprocity Laws
  • Hilbert Class Fields over Imaginary Quadratic Fields
  • Indefinite Modular Forms
  • Dimension Formulas in the Case of Weight 1
  • 2-Dimensional Galois Representations of Odd Type and Non-Dihedral Cusp Forms of Weight 1
  • Maass Cusp Forms of Eigenvalue 1/4
  • Selberg's Eigenvalue Conjecture and the Ramanujan-Petersson Conjecture
  • Indefinite Theta Series
  • Hilbert Modular Forms of Weight 1
  • Appendix A: Some Dimension Formula and Traces of Hecke Operators for Cusp Forms of Weight 1

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