Number theory arithmetic in Shangri-La : proceedings of the 6th China-Japan seminar, Shanghai, China, 15-17 August, 2011 / editors, Shigeru Kanemitsu, Kinki University, Japan, Hongze Li, Shanghai Jiao Tong University, China, Jianya Liu, Shandong University, China.

Format:

Book

Conference/Event

Author/Creator:

China-Japan Seminar on Number Theory, Corporate Author.

Contributor:

Kanemitsu, Shigeru, editor.

Li, Hongze, editor.

Liu, Jianya, editor.

Conference Name:

China-Japan Seminar (6th : 2011 : Shanghai, China)

China-Japan Seminar on Number Theory.

Series:

Series on number theory and its applications ; v. 8.

Language:

English

Subjects (All):

Number theory--Congresses.

Number theory.

Physical Description:

1 online resource (xii, 260 pages) : illustrations.

Place of Publication:

Singapore : World Scientific Pub. Co., 2013.

New Jersey : World Scientific, [2013]

Language Note:

English

Summary:

This volume is based on the successful 6th China-Japan Seminar on number theory that was held in Shanghai Jiao Tong University in August 2011. It is a compilation of survey papers as well as original works by distinguished researchers in their respective fields. The topics range from traditional analytic number theory - additive problems, divisor problems, Diophantine equations - to elliptic curves and automorphic L-functions. It contains new developments in number theory and the topics complement the existing two volumes from the previous seminars which can be found in the same book series.

Contents:

Preface; CONTENTS; On Jacobi Forms with Levels Hiroki Aoki; 1. Definitions and basic properties; 1.1. Elliptic modular forms; 1.2. Siegel modular forms of degree 2; 1.3. Jacobi forms; 1.4. Jacobi forms with levels; 1.5. Theta decomposition; 1.6. Structure theorem for weak Jacobi forms; 2. Applications; 2.1. Structure of Siegel modular forms; 2.2. Formal series of Jacobi forms; 2.3. Index-Level change of Jacobi forms; Acknowledgements; References; Additive Representation in Thin Sequences, VIII: Diophantine Inequalities in Review Jorg Brudern, Koichi Kawada and Trevor D. Wooley

1. Theme and results1.1. Diophantine inequalities; 1.2. Additive cubic forms; 1.3. Linear forms in primes; 1.4. Further applications; 1.5. A related diophantine inequality; 2. The Fourier transform method; 2.1. Some classical integrals; 2.2. Counting solutions of diophantine inequalities; 2.3. Weighted counting; 2.4. The central interval; 2.5. The interference principle; 3. Classical mean square methods; 3.1. Plancherel's identity; 3.2. Some mean values; 3.3. The amplification technique; 3.4. Linear forms in primes; 3.5. Bessel's inequality; 4. Semi-classical averaging

4.1. Another mean square approach4.2. Exponential sums over test sequences; 4.3. Potential applications; 5. Fourier analysis of exceptional sets; 5.1. An illustrative example; 5.2. A quadratic average; 5.3. Some brief heckling; 5.4. An inequality involving quadratic polynomials; 5.5. An application of Vinogradov's method; 5.6. Linear forms in primes, yet again; 6. Outstanding arts; 6.1. Smooth cubic Weyl sums; 6.2. Senary cubic forms; 6.3. Two technical estimates; 6.4. The lower bound variant; 6.5. An auxiliary inequality; 6.6. Additive forms of large degree; 6.7. Proof of Theorem 1.8

6.8. Proof of Theorem 1.97. An appendix on inhomogeneous polynomials; 7.1. The counting integral; 7.2. The central interval; 7.3. The complementary compositum; Acknowledgements; References; Annexe to the Gallery: An Addendum to "Additive Representation in Thin Sequences, VIII: Diophantine Inequalities in Review" Jorg Brudern, Koichi Kawada and Trevor D. Wooley; 11. Downloading updates; References; A Note on the Distribution of Primes in Arithmetic Progressions Zhen Cui and Boqing Xue; 1. Introduction; 2. Notations and Some Lemmas; 3. Proofs; 4. Further Remark; Acknowledgements; References

Matrices of Finite Abelian Groups, Finite Fourier Transform and Codes Shigeru Kanemitsu and Michel Waldschmidt1. The matrix of a finite abelian group; 1.1. Matrix of a finite group; 1.2. Matrix of a finite abelian group; 1.3. Matrix of a cyclic group; 1.4. The group ring of a cyclic group and the algebra of circulants; 1.5. The group ring F[G] of a finite abelian group G; 2. Finite Fourier Transform associated with a finite abelian group; 2.1. Generalized Finite Fourier Transform; 2.2. Case of a cyclic group: Finite Fourier Transform; 3. Hamming weight and Generalized Finite Fourier Transform

4. The matrix of a finite group

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9781299462762

1299462766

9789814452458

9814452459

OCLC:

840495762