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

• 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
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• 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 / 平均値定理 / 指数対 / 一般約数問題 / 約数問題 / 円問題 / 生成関数の微分化

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.

Research Products

• [Journal Article] On a new circle problem (2017)
  • Author(s): Jun Furuya, Makoto Minamide, Yoshio Tanigawa
  • Journal Title: Journal of the Australian Mathematical Society Volume: 印刷中 Issue: 2 Pages: 231-249
  • DOI: 10.1017/s1446788716000525
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] On a restricted divisor problem (2016)
  • Author(s): Jun Furuya, Makoto Minamide, Yoshio Tanigawa
  • Journal Title: Journal of Indian Mathematical Society Volume: 83 Pages: 269-287
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Presentation] ζ(s)ζ´(s), ζ(s)ζ´´(s), ζ´(s)ζ´´(s) の近似関数等式について (2017)
  • Author(s): 南出真、古屋淳、谷川好男
  • Organizer: 日本数学会年会代数分科会
  • Place of Presentation: 首都大学東京
  • Year and Date: 2017-03-24
• [Presentation] 条件付きメビウス関数の和について (2017)
  • Author(s): 南出真、古屋淳、谷川好男
  • Organizer: 日本数学会中国四国支部例会
  • Place of Presentation: 愛媛大学
  • Year and Date: 2017-01-22
• [Presentation] ζ´(s)2 の近似関数等式について (2016)
  • Author(s): 南出真、古屋淳、谷川好男
  • Organizer: 日本数学会秋季総合分科会代数分科会
  • Place of Presentation: 関西大学
  • Year and Date: 2016-09-17
• [Presentation] 制限約数問題について (2016)
  • Author(s): 谷川好男、古屋淳、南出真
  • Organizer: 日本数学会２０１６年度年会・代数分科会
  • Place of Presentation: 筑波大学
  • Year and Date: 2016-03-16
• [Presentation] 円問題および一般約数問題の微分化 (2016)
  • Author(s): 古屋淳、南出真、谷川好男
  • Organizer: 平成２７年度日本数学会中国四国支部例会
  • Place of Presentation: 広島大学
  • Year and Date: 2016-01-24
• [Presentation] 微分円問題における有限型 Voronoi 公式 (2015)
  • Author(s): 南出真、古屋淳、谷川好男
  • Organizer: 日本数学会２０１５年度秋季総合分科会・代数分科会
  • Place of Presentation: 京都産業大学
  • Year and Date: 2015-09-13