Number Theoretic Methods

1. Front Matter

   Pages i-xi

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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

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.

• Algebra
• Arithmetic
• Finite
• Identity
• Prime
• equation
• function
• mathematics
• number theory
• theorem

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

  Shigeru Kanemitsu

• Institute of Mathematics, Academia Sinica, Beijing, China

  Chaohua Jia

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