On reseaches of several properties of Dirichlet series and its related fields

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400030
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Hamamatsu University School of Medicine
• Principal Investigator: Furuya Jun 浜松医科大学, 医学部, 教授 (10413890)
• Co-Investigator(Renkei-kenkyūsha): Minamide Makoto 山口大学, 理工学研究科, 講師 (80596552) ; Tanigawa Yoshio 名古屋大学, 多元数理科学研究科, 招へい教員 (50109261)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: ディリクレ級数 / 近似関数等式 / ガウスの円問題 / 周期的ベルヌーイ関数 / 数論的誤差項

Outline of Final Research Achievements

We study the analytic properties of Dirichlet series and its related topics, which are considered as one of the most important problem in number theory.In particular, we derive (1) approximate functional equations of the product of derivatives of the Riemann zeta-functions (2) representation formulas of number-theoretic error terms related to the summation formula of the arithmetical function whose generating function is related to derivatives of some Dirichlet series, and non-trivial estimates of these error terms (3) truncated Voronoi formulas and mean value theorems for several number-theoretic error terms.

Free Research Field

解析的整数論