## Analytic Number TheoryChaohua Jia, Kohji Matsumoto 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. |

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### Contents

II | 1 |

III | 17 |

IV | 27 |

V | 39 |

VI | 93 |

VII | 99 |

VIII | 121 |

IX | 127 |

XIV | 195 |

XV | 205 |

XVI | 223 |

XVII | 243 |

XVIII | 269 |

XIX | 277 |

XX | 303 |

XXI | 349 |

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2002 Kluwer Academic abelian surfaces Acta Arith algebraic number analytic continuation Analytic Number Theory apply asymptotic Bernoulli polynomial class number CM-field coefficients completes the proof congruence consider constant Corollary Dedekind define denote Diophantine Dirichlet character Dirichlet L-functions E-periodic error term estimate exists expansion finite fixed point Fujii functional equation G Zs Hence Hurwitz zeta function implies inequality inteyer irrationality measure Iwaniec Kluwer Academic Publishers Kronecker limit formula Lemma Lemmata limit formula London Math Mathematics Subject Classification matrix Matsumoto eds mean value modulo multiple natural number non-E-periodic Note number field number of solutions obtain Pade approximation partition positive integer positive number prime factor prime number proof of Theorem Proposition prove quadratic real number Remark resp result Riemann right-hand side satisfying Section sequence singularities substitution Suppose Thue equations uniform map upper bound zeros zeta-function zeta-regularization