Number theory : sailing on the sea of number theory : proceedings of the 4th China-Japan Seminar, Weihai, China, 30 August - 3 September, 2006 / editors, S. Kanemitsu, J.-Y. Liu.

Format:

Book

Conference/Event

Author/Creator:

China-Japan Seminar on Number Theory, Corporate Author.

Contributor:

Kanemitsu, Shigeru.

Liu, J. Y.

Conference Name:

China-Japan Seminar on Number Theory (4th : 2006 : Weihai, China)

China-Japan Seminar on Number Theory

Series:

Series on Number Theory & Its Applications

Series on number theory and its applications ; v. 2

Language:

English

Subjects (All):

Number theory--Congresses.

Number theory.

Algebra--Congresses.

Algebra.

Physical Description:

1 online resource (268 p.)

Place of Publication:

Singapore ; Hackensack, NJ : World Scientific, c2007.

Language Note:

English

Summary:

This volume is not an ordinary proceedings volume assembling papers submitted but a collection of prestigious survey papers on various subjects studied enthusiastically by experts all over the world. The reader will uncover profound, new research problems as well as numerous signposts for future direction.

Contents:

Preface; Program; Contents; Convolutions of the von Mangoldt Function and Related Dirichlet Series Shigeki Egami and Kohji Matsumoto; 1. The analytic continuation of multiple Dirichlet series; 2. An example of double Dirichlet series with a natural boundary; 3. Proof of Theorem 2.1; 4. Proof of Theorem 2.2; 5. An application to the Riesz mean; 6. The multiple case; References; Constructing New Non-congruent Numbers by Graph Theory Keqin Feng and Yan Xue; 1. Introduction; 2. Selmer groups; 3. Oddness of graphs; 4. New non-congruent numbers; 5. Birch and Swinnerton-dyer conjecture for En

ReferencesDistribution of Units of an Algebraic Number Field Modulo an Ideal Yoshiyuki Kitaoka; 1. Introduction; 2. Case of prime ideals; 2.1. Polynomial g(x); 2.2. Upper bound for #E(p); 2.3. Conjecture; 3. Case of rational primes; 3.1. Structure of o as an η-module; 3.2. Relη and κ(η); 3.3. Evaluation of κ(η); 3.3.1. Action of automorphisms; 3.3.2. Evaluation of κ(η); 4. Examples; 4.1. Case of η = id; 4.1.1. Case of real quadratic fields; 4.1.2. Case of real cubic abelian fields; 4.1.3. Case of non-cyclic abelian fields of degree 4; 4.1.4. Case of imaginary abelian fields of degree 4

4.1.5. Case where F is the Galois closure of a real cubic field F0 with negative discriminant4.2. Case of complex conjugation; 4.2.1. Case of [F : Q] = 4; 4.2.2. Case of [F : Q] = 6; 4.3. Case where F is an imaginary abelian field with [F : Q] = 6 and the order of Gal(F/Q) is 3; 5. Appendix; 5.1. Divisors of f(p); 5.2. Structure of Galois group extended by roots of units; Acknowledgments; References; Sign Changes of Fourier Coefficients and Eigenvalues of Cusp Forms Winfried Kohnen; 1. Introduction; 2. The starting point; 3. Elliptic modular forms; 4. Siegel modular forms of genus two

ReferencesShifted Convolution Sums of Fourier Coefficients of Cusp Forms Yuk-Kam Lau, Jianya Liu and Yangbo Ye; 1. Automorphic L-functions and subconvexity problems; 1.1. The classical case: the Riemann zeta-function and Dirichlet L-functions; 1.2. L-functions of degree two; 1.3. Rankin-Selberg L-functions; 1.4. Plan of the article; 1.5. Notations; 2. Shifted convolution sums; 2.1. Spectral theory of automorphic forms; 2.2. The Rankin-Selberg method and shifted convolution sums; 3. Variants of the circle method; 3.1. The δ-symbol method; 3.2. Jutila's variant; 4. The spectral method

5. The spectral method: meromorphic continuation to σ > 1/26. Spectral method: meromorphic continuation to σ > 1/2; 6.1. Further meromorphic continuation to σ > 1/2; 6.2. Illustration for the proof of Theorem 1.1; References; Two Expositions on Arithmetic of Cubics Katsuya Miyake; 1. Introduction; 2. Part I: Generic polynomials of degree 3; 2.1. Generic polynomials of degree 3; 2.2. The Splitting Field of R(t; X); 2.3. A Criterion for Kt Kt; 2.4. Notes on the Reducible Cases; 2.5. An Application: Parametrization of Unrami.ed Cyclic Cubic Extensions of Quadratic Fields

3. Part II: Some Families of Elliptic Curves related with Cubic Fields

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786611919016

9781281919014

1281919012

9789812770134

9812770135