Additive number theory of symmetric matrices
Project/Area Number  09640020 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
Algebra

Research Institution  Toyama University 
Principal Investigator 
EGAMI Shigeki Toyama University, Department of Engineering, Associate Professor., 工学部, 助教授 (60168771)

CoInvestigator(Kenkyūbuntansha) 
NAKAI Yoshinobu Yamanashi University, Department of Education and Human Sciences, Professor., 教育学部, 教授 (40022652)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥1,300,000 (Direct Cost : ¥1,300,000)
Fiscal Year 1998 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1997 : ¥800,000 (Direct Cost : ¥800,000)

Keywords  additive number theory / spectral theory of automorphic forms / trigonometric sums / multiple zeta function / 加法的整数論 / 保型形式のスペクトル理論 / 三角和 / 多重ゼータ関数 / 加法的数論 / ワイル和 / Dirichlet級数 / 分割問題 / 保型形式 / スペクトル分解 / エルゴード理論 
Research Abstract 
The purposes of our investigation is to develop analytic number theory of matrices through spectral theory of automorphic forms, trigonometric sums, and padic methods. Investigations of the methods themselves and applications to other problems in number theory are also contained in our project. In 1997, using trigonometric sums and padic method Egami obtained a result on finite dynamical systems, which was reported in a conference held in York U.K.. He also investigated a problem of Mitsui and resolved degree 2 case. This result was reported at a conference in number theory held at Kyoto in Novenber. Moreover Nakai (with Shiokawa) applied trigonometric sums to the problem of values of polynomials at primes. In 1998, Egami investigated multiple zeta functions and its generalizations , which are expected to give an elementary approach to Mitsui's problem. Nakai created the theory of cubic theta sums, which is expected to be a powerful tool for additive number theory. Both of the results were reported at a conference of number theory held at Kyoto in Octorber.

Report
(4results)
Research Output
(12results)