Number theory : dreaming in dreams : proceedings of the 5th China-Japan Seminar : Higashi-Osaka, Japan 27-31 August 2008 / editors, Takashi Aoki, Shigeru Kanemitsu, Jianya Liu.

Format:

Book

Conference/Event

Author/Creator:

China-Japan Seminar on Number Theory, Corporate Author.

Contributor:

Aoki, Takashi, 1953-

Kanemitsu, Shigeru.

Liu, Jianya.

Conference Name:

China-Japan Seminar on Number Theory (5th : 2008 : Higashiōsaka-shi, Japan)

China-Japan Seminar on Number Theory.

Series:

Series on number theory and its applications ; v. 6.

Series on number theory and its applications, 1793-3161 ; v. 6

Language:

English

Subjects (All):

Number theory--Congresses.

Number theory.

Physical Description:

1 online resource (267 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; Hackensack, N.J. : World Scientific, 2010.

Language Note:

English

Summary:

This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory. Kitaoka's paper is a continuation of his earlier paper published in the last proceedings and pushes the research forward. Browning's paper introduces a new direction of research on analytic number theory - quantitative theory of some surfaces and Bruedern et al's paper details state-of-the-art affairs of additive number theory. There are two papers on modular forms - Kohnen's paper describes generalized modular forms (GMF) which has some applications in conformal f

Contents:

""CONTENTS""; ""Preface""; ""Recent progress on the quantitative arithmetic of del Pezzo surfaces Tim D. Browning""; ""1. Introduction""; ""Acknowledgements""; ""2. Geometry of V0""; ""3. Overview of the proof""; ""3.1. Reduction to conics of low height""; ""3.2. Parametrisation of the conics""; ""3.3. Lattice point counting in the plane""; ""3.4. Divisor problem for binary forms""; ""3.5. Comparison with Peyre�s constant""; ""4. Further exploration""; ""References""

""Additive representation in thin sequences, VIII: Diophantine inequalities in review Jorg Brudern, Koichi Kawada and Trevor D. Wooley""""1. Theme and results""; ""1.1. 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 approach""; ""4.2. 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 1.9""; ""7. An appendix on inhomogenous polynomials""; ""7.1. The counting integral""; ""7.2. The central interval""; ""7.3. The complementary compositum""; ""Acknowledgements""; ""References""; ""Recent progress on dynamics of a special arithmetic function Chaohua Jia""

""1. Introduction""""2. Dynamics of the w function""; ""3. Inverse problem""; ""4. The sketch of the proof of Theorem 3.5""; ""5. Acknowledgements""; ""References""; ""Some Diophantine problems arising from the isomorphism problem of generic polynomials Akinari Hoshi and Katsuya Miyake""; ""1. Introduction""; ""2. Some results: the cubic case""; ""3. A parametric family of Thue equations""; ""4. The case of D4""; ""5. Numerical examples: the case of C4""; ""6. Numerical examples: the case of D5""; ""7. Appendix""; ""References""

""A statistical relation of roots of a polynomial in different local fields II Yoshiyuki Kitaoka""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786612761782

9781282761780

1282761781

9789814289924

9814289922

OCLC:

630153519