Analytic Number Theory

1. Front Matter

   Pages i-xv

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2. On Analytic Continuation of Multiple L-Functions and Related Zeta-Functions

   • Shigeki Akiyama, Hideaki Ishikawa

   Pages 1-16

3. On the Values of Certain q-Hypergeometric Series II

   • Masaaki Amou, Masanori Katsurada, Keijo Väänänen

   Pages 17-25

4. The Class Number One Problem for Some Non-Normal Sextic CM-Fields

   • Gérard Boutteaux, Stéphane Louboutin

   Pages 27-37

5. Ternary Problems in Additive Prime Number Theory

   • Jörg Brüdern, Koichi Kawada

   Pages 39-91

6. A Generalization of E. Lehmer’s Congruence and Its Applications

   • Tianxin Cai

   Pages 93-98

7. On Chen’s Theorem

   • Yingchun Cai, Minggao Lu

   Pages 99-119

8. On a Twisted Power Mean of L(1, χ)

   • Shigeki Egami

   Pages 121-125

9. On the Pair Correlation of the Zeros of the Riemann Zeta Function

   • Akio Fujii

   Pages 127-142

10. Discrepancy of Some Special Sequences

    • Kazuo Goto, Yukio Ohkubo

    Pages 143-155

11. Padé Approximation to the Logarithmic Derivative of the Gauss Hypergeometric Function

    • Masayoshi Hata, Marc Huttner

    Pages 157-172

12. The Evaluation of the Sum over Arithmetic Progressions for the Coefficients of the Rankin-Selberg Series II

    • Yumiko Ichihara

    Pages 173-182

13. Substitutions, Atomic Surfaces, and Periodic Beta Expansions

    • Shunji Ito, Yuki Sano

    Pages 183-194

14. The Largest Prime Factor of Integers in the Short Interval

    • Chaohua Jia

    Pages 195-203

15. A General Divisor Problem in Landau’s Framework

    • S. Kanemitsu, A. Sankaranarayanan

    Pages 205-221

16. On Inhomogeneous Diophantine Approximation and the Borweins’ Algorithm, II

    • Takao Komatsu

    Pages 223-242

17. Asymptotic Expansions of Double Gamma-Functions and Related Remarks

    • Kohji Matsumoto

    Pages 243-268

18. A Note on a Certain Average of L(1/2 +it, χ)

    • Leo Murata

    Pages 269-276

19. On Covering Equivalence

    • Zhi-Wei Sun

    Pages 277-302

20. Certain Words, Tilings, Their Non-Periodicity, and Substitutions of High Dimension

    • Jun-ichi Tamura

    Pages 303-348

From September 13 to 17 in 1999, the First China-Japan Seminar on Number Theory was held in Beijing, China, which was organized by the Institute of Mathematics, Academia Sinica jointly with Department of Mathematics, Peking University. TE:m Japanese Professors and eighteen Chinese Professors attended this seminar. Professor Yuan Wang was the chairman, and Professor Chengbiao Pan was the vice-chairman. This seminar was planned and prepared by Professor Shigeru Kanemitsu and the first-named editor. Talks covered various research fields including analytic number theory, algebraic number theory, modular forms and transcendental number theory. The Great Wall and acrobatics impressed Japanese visitors. From November 29 to December 3 in 1999, an annual conference on analytic number theory was held in Kyoto, Japan, as one of the conferences supported by Research Institute of Mathematical Sciences (RIMS), Kyoto University. The organizer was the second-named editor. About one hundred Japanese scholars and some foreign visitors com­ ing from China, France, Germany and India attended this conference. Talks covered many branches in number theory. The scenery in Kyoto, Arashiyama Mountain and Katsura River impressed foreign visitors. An informal report of this conference was published as the volume 1160 of Surikaiseki Kenkyusho Kokyuroku (June 2000), published by RIMS, Ky­ oto University. The present book is the Proceedings of these two conferences, which records mainly some recent progress in number theory in China and Japan and reflects the academic exchanging between China and Japan.

• Arithmetic
• Diophantine approximation
• Prime
• average
• equation
• function
• number theory
• prime number
• theorem

• Academia Sinica, China

  Chaohua Jia

• Nagoya University, Japan

  Kohji Matsumoto

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