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