Non-Euclidean Structure of the family of zeta-functions
Grant-in-Aid for Scientific Research (C)
|Research Institution||Nihon University|
MOTOHASHI Yoichi Nihon Univ., College of Sci.Techn.Department of Mathematics, Professor, 理工学部, 教授 (30059969)
|Project Fiscal Year
1995 – 1996
Completed(Fiscal Year 1996)
|Budget Amount *help
¥2,200,000 (Direct Cost : ¥2,200,000)
Fiscal Year 1996 : ¥1,400,000 (Direct Cost : ¥1,400,000)
Fiscal Year 1995 : ¥800,000 (Direct Cost : ¥800,000)
|Keywords||zeta-function / hyperbolic geometry / spectral analysis / trace-formulas / ゼータ関数 / 非ユークリッド空間 / スペクトル理論 / 跡公式 / スペクトル解析 / 素数分布論|
The aim of my project was to extend, to certain family of zeta-functions, the findings that had been obtained by myself in an extensive study of the Riemann zeta-function. In particular, the main object of the research was to analyze a hyperbolic (i.e., non-Euclidean) structure that seemed to govern the whole family, which should open a new perspective over the entire theory of zeta-functions.
To these effects, we obtained :
(1) A new proof of Kuznetsou's trace-formula over the hyperbolic upper-half-space.
(2) A proof of the trace formula over the hyperbolic upper-half-space.
(3) A new relation between Dedekind zeta-functions of quadratic number fields and Hecke congruence groups.
Those results were reported as invited lectures at
(i) The 39th Taniguchi International Symposium (organized by Y.Motohashi) : 1996
(ii) International Symposium on Analytic Number Theory (organized by Hong Kong Univ.) : 1997
(iii) International Symposium on Analytic Number Theory (organized by Polish Academy) : 1997
Further, it should be noted that the whole research result was published by Cambridge University Press in a volume of their Mathematical Tracts Series.
Research Output (26results)