An Introduction to Non-Abelian Class Field Theory

Automorphic Forms of Weight 1 and 2-Dimensional Galois Representations

Nonfiction, Science & Nature, Mathematics, Arithmetic, Number Theory
Cover of the book An Introduction to Non-Abelian Class Field Theory by Toyokazu Hiramatsu, Seiken Saito, World Scientific Publishing Company
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Toyokazu Hiramatsu, Seiken Saito ISBN: 9789813142282
Publisher: World Scientific Publishing Company Publication: September 13, 2016
Imprint: WSPC Language: English
Author: Toyokazu Hiramatsu, Seiken Saito
ISBN: 9789813142282
Publisher: World Scientific Publishing Company
Publication: September 13, 2016
Imprint: WSPC
Language: English

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.

Contents:

  • Part I:

    • Higher Reciprocity Laws
    • Hilbert Class Fields over Imaginary Quadratic Fields
    • Indefinite Modular Forms
    • Dimension Formulas in the Case of Weight 1
  • Part II:

    • 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: Some Dimension Formula and Traces of Hecke Operators for Cusp Forms of Weight 1 — Göttingen talk, 1989. By Toyokazu Hiramatsu

Readership: Advanced undergraduate and graduate students, and researchers in number theory.
Key Features:

  • The monograph provides a comprehensive overview of the author's works which include new contributions, such as dimension formulas in the case of weight 1 forms, some relations between higher reciprocity laws of non-abelian polynomials and Langlands' reciprocity laws
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

Contents:

Readership: Advanced undergraduate and graduate students, and researchers in number theory.
Key Features:

More books from World Scientific Publishing Company

Cover of the book Modeling and Pricing in Financial Markets for Weather Derivatives by Toyokazu Hiramatsu, Seiken Saito
Cover of the book Pioneers of Medicine Without a Nobel Prize by Toyokazu Hiramatsu, Seiken Saito
Cover of the book George Placzek by Toyokazu Hiramatsu, Seiken Saito
Cover of the book Harmful Natural Chemicals and Radiation in the Environment by Toyokazu Hiramatsu, Seiken Saito
Cover of the book Cyclodextrins by Toyokazu Hiramatsu, Seiken Saito
Cover of the book An Introduction to Knowledge Information Strategy by Toyokazu Hiramatsu, Seiken Saito
Cover of the book Singapore Teachers by Toyokazu Hiramatsu, Seiken Saito
Cover of the book Beam Dynamics in High Energy Particle Accelerators by Toyokazu Hiramatsu, Seiken Saito
Cover of the book Conformational Concept for Synthetic Chemist's Use by Toyokazu Hiramatsu, Seiken Saito
Cover of the book Flexoelectricity in Solids by Toyokazu Hiramatsu, Seiken Saito
Cover of the book Introduction to Electricity and Magnetism by Toyokazu Hiramatsu, Seiken Saito
Cover of the book Frontiers in Electronics by Toyokazu Hiramatsu, Seiken Saito
Cover of the book The Langevin Equation by Toyokazu Hiramatsu, Seiken Saito
Cover of the book Dark Energy by Toyokazu Hiramatsu, Seiken Saito
Cover of the book Nutrition, Epigenetics and Health by Toyokazu Hiramatsu, Seiken Saito
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy