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Number Theoretic Methods

Future Trends

  • Book
  • © 2002

Overview

Editors:
  1. Shigeru Kanemitsu

    1. Graduate School of Advanced Technology, University of Kinki, Iizuka, Japan

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  2. Chaohua Jia

    1. Institute of Mathematics, Academia Sinica, Beijing, China

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Developments in Mathematics (DEVM, volume 8)

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Table of contents (22 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. A Limiting form of the q-Dixon 4φ3 Summation and Related Partition Identities

    • Krishnaswami Alladi, Alexander Berkovich
    Pages 1-14

  3. Arithmetical Properties of Solutions of Linear Second Order q-Difference Equations

    • Masaaki Amou, Tapani Matala-aho
    Pages 15-29

  4. Ramanujan’s Contributions to Eisenstein Series, Especially in His Lost Notebook

    • Bruce C. Berndt, Ae Ja Yee
    Pages 31-53

  5. New Applications of a Result of Galochkin on Linear Independence

    • Peter Bundschuh
    Pages 55-66

  6. Partitions Modulo Prime Powers and Binomial Coefficients

    • Tianxin Cai
    Pages 67-72

  7. Infinite Sums, Diophantine Equations and Fermat’s Last Theorem

    • Henri Darmon, Claude Levesque
    Pages 73-95

  8. On the Nature of the “Explicit Formulas” in Analytic Number Theory — A Simple Example

    • Christopher Deninger
    Pages 97-118

  9. Product Representations by Rationals

    • P. D. T. A. Elliott
    Pages 119-150

  10. On the Distribution of αp Modulo One

    • Chaohua Jia
    Pages 151-157

  11. Ramanujan’s Formula and Modular Forms

    • Shigeru Kanemitsu, Yoshio Tanigawa, Masami Yoshimoto
    Pages 159-212

  12. Waldspurger’s Formula and Central Critical Values of L-Functions of Newforms in Weight Aspect

    • Winfried Kohnen, Jyoti Sengupta
    Pages 213-217

  13. Primitive Roots: A Survey

    • Shuguang Li, Carl Pomerance
    Pages 219-231

  14. Zeta-Functions Defined by Two Polynomials

    • Kohji Matsumoto, Lin Weng
    Pages 233-262

  15. Some Aspects of Interactions between Algebraic Number Theory and Analytic Number Theory

    • Katsuya Miyake
    Pages 263-299

  16. On G-Functions and Padé Approximations

    • Makoto Nagata
    Pages 301-310

  17. A Penultimate Step toward Cubic Theta-Weyl Sums

    • Yoshinobu Nakai
    Pages 311-338

  18. Some Results in View of Nevanlinna Theory

    • Junjiro Noguchi
    Pages 339-350

  19. A Historical Comment about the GVT in Short Interval

    • Chengbiao Pan
    Pages 351-367

  20. Convexity and Intersection of Random Spaces

    • Mariya Shcherbina, Brunello Tirozzi
    Pages 369-380
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Keywords

About this book

This volume contains the proceedings of the very successful second China-Japan Seminar held in lizuka, Fukuoka, Japan, during March 12-16, 2001 under the support of the Japan Society for the Promotion of Science (JSPS) and the National Science Foundation of China (NSFC), and some invited papers of eminent number-theorists who visited Japan during 1999-2001 at the occasion of the Conference at the Research Institute of Mathematical Sciences (RIMS), Kyoto University. The proceedings of the 1st China-Japan Seminar held in September 1999 in Beijing has been published recently {2002) by Kluwer as DEVM 6 which also contains some invited papers. The topics of that volume are, however, restricted to analytic number theory and many papers in this field are assembled. In this volume, we return to the lines of the previous one "Number Theory and its Applications", published as DEVM 2 by Kluwer in 1999 and uphold the spirit of presenting various topics in number theory and related areas with possible applica­ tions, in a unified manner, and this time in nearly a book form with a well-prepared index. We accomplish this task by collecting highly informative and readable survey papers (including half-survey type papers), giving overlooking surveys of the hith­ erto obtained results in up-to-the-hour form with insight into the new developments, which are then analytically continued to a collection of high standard research papers which are concerned with rather diversed areas and will give good insight into new researches in the new century.

Editors and Affiliations

  • Graduate School of Advanced Technology, University of Kinki, Iizuka, Japan

    Shigeru Kanemitsu

  • Institute of Mathematics, Academia Sinica, Beijing, China

    Chaohua Jia

Bibliographic Information

  • Book Title: Number Theoretic Methods

  • Book Subtitle: Future Trends

  • Editors: Shigeru Kanemitsu, Chaohua Jia

  • Series Title: Developments in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-3675-5

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2002

  • Hardcover ISBN: 978-1-4020-1080-4Published: 31 December 2002

  • Softcover ISBN: 978-1-4419-5239-4Published: 07 December 2010

  • eBook ISBN: 978-1-4757-3675-5Published: 14 March 2013

  • Series ISSN: 1389-2177

  • Series E-ISSN: 2197-795X

  • Edition Number: 1

  • Number of Pages: XI, 441

  • Topics: Number Theory, Algebra, Mathematics, general

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