Analytic properties of automorphic L-functins

2015 Fiscal Year Final Research Report

• Project/Area Number: 26887035
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Josai University (2015); Tokyo Denki University (2014)
• Principal Investigator: Sono Keiju 城西大学, 理学部, 助教 (10735989)
• Project Period (FY): 2014-08-29 – 2016-03-31
• Keywords: ゼータ関数 / L-関数 / 保型形式 / 素数分布 / リーマン予想

Outline of Final Research Achievements

During these two years I have studied the following two objects. The first is the evaluation of the rate of simple zeros of Dirichlet L-functions, and the second is the evaluation of the moments of quadratic twists of automorphic L-functions at the central point. I proved that assuming the generalized Riemann hypothesis, at least 93％ of zeros of primitive Dirichlet L-functions are simple. In the second theme, assuming several hypotheses, I proved that these moments are bounded by the expected order. I have talked about these results at several symposiums in Japan. I have submitted two papers on these results to some international journals and fortunately the papers were accepted.

Free Research Field

解析的整数論