Description

Book Synopsis
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.

Table of Contents
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;

Introduction To Non-abelian Class Field Theory,

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    A Hardback by Toyokazu Hiramatsu, Seiken Saito

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      View other formats and editions of Introduction To Non-abelian Class Field Theory, by Toyokazu Hiramatsu

      Publisher: World Scientific Publishing Co Pte Ltd
      Publication Date: 08/11/2016
      ISBN13: 9789813142268, 978-9813142268
      ISBN10: 981314226X

      Description

      Book Synopsis
      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.

      Table of Contents
      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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