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素数の加法的問題,特にその例外集合について

Research Project

Project/Area Number 16J00906
Research Category

Grant-in-Aid for JSPS Fellows

Allocation TypeSingle-year Grants
Section国内
Research Field Algebra
Research InstitutionNagoya University

Principal Investigator

鈴木 雄太  名古屋大学, 多元数理科学研究科, 特別研究員(DC1)

Project Period (FY) 2016-04-22 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2018: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2017: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2016: ¥900,000 (Direct Cost: ¥900,000)
Keywords指数和 / 数論的関数 / Vinogradov平均値定理 / Lambert級数 / 無理数性 / 加法的整数論 / 素数分布論 / Hurwitz zeta / 友愛数 / Graph Ramsey Number
Outline of Annual Research Achievements

昨年度終わりから行っていた数論的関数の平均値のWalfisz型誤差項評価の研究についてプレプリントを公表した. 特に, Vinogradov型の組合せ論的分解を改良し用いることで, H.-Q. LiuによるEuler totient関数に対する結果を拡張することができた. 関連して, あるクラスのtotient関数の平均値について, Max Planck Institute for MathematicsのPieter Moree氏, Alisa Sedunova氏とJohannes Kepler University of LinzのSumaia Saad Eddin氏との共同研究を行い, 円分多項式の種々の特殊値の平均値の計算に成功した. オーストリア滞在中には別テーマではあるがSumaia Saad Eddin氏との「条件付きの素数2つの積」に関する研究も大枠の進展を見た.
また新たなテーマとして, 弘前大学の立谷洋平氏とBaggio Engineering SchoolのDaniel Duverney 氏と整除性に関連したLambert 級数の無理数性について共同研究を始めた. Lambert級数は約数関数に類する数論的関数を含むべき級数へ変形することができる. ここにErdosが用いた無理性判定のための手法を用いるのだが, この際数論的関数の局所的な振る舞いをコントロールする必要がある. このような数論的関数の局所的振る舞いは難しいので, 残念ながら素数列に渡るLambert級数は取り扱えないが, 素数よりもう少し疎な2項ずつ互いに素な数列に渡るLambert級数を簡単な篩法を用いてコントロールすることに成功した. 現在までに得られている結果を用いれば, 例えば素数の2乗番目のFibonacci数の逆数和は無理数であることがわかる.

Research Progress Status

平成30年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

平成30年度が最終年度であるため、記入しない。

Report

(3 results)
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • Research Products

    (41 results)

All 2019 2018 2017 2016 Other

All Int'l Joint Research (7 results) Journal Article (6 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 6 results) Presentation (28 results) (of which Int'l Joint Research: 6 results,  Invited: 3 results)

  • [Int'l Joint Research] Max Planck Institute for Mathematics(ドイツ)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Johannes Kepler University of Linz(オーストリア)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Baggio Engineering School(フランス)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] リール第一大学(フランス)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] デュッセルドルフ大学(ドイツ)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] リール第一大学(フランス)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] デュッセルドルフ大学(ドイツ)

    • Related Report
      2016 Annual Research Report
  • [Journal Article] The graph Ramsey number R(Fl,K6)2019

    • Author(s)
      Kadota Shin-ya、Onozuka Tomokazu、Suzuki Yuta
    • Journal Title

      Discrete Mathematics

      Volume: 342 Issue: 4 Pages: 1028-1037

    • DOI

      10.1016/j.disc.2018.12.016

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Real zeros of Hurwitz zeta-functions and their asymptotic behavior in the interval (0,1)2019

    • Author(s)
      Endo Kenta、Suzuki Yuta
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 473 Issue: 2 Pages: 624-635

    • DOI

      10.1016/j.jmaa.2018.12.001

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] GOLDBACH REPRESENTATIONS IN ARITHMETIC PROGRESSIONS AND ZEROS OF DIRICHLET L-FUNCTIONS2018

    • Author(s)
      Bhowmik Gautami、Halupczok Karin、Matsumoto Kohji、Suzuki Yuta
    • Journal Title

      Mathematika

      Volume: 65 Issue: 1 Pages: 57-97

    • DOI

      10.1112/s0025579318000323

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On amicable tuples2018

    • Author(s)
      Suzuki Yuta
    • Journal Title

      Illinois Journal of Mathematics

      Volume: 62 Issue: 1-4 Pages: 225-252

    • DOI

      10.1215/ijm/1552442661

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A remark on the conditional estimate for the sum of a prime and a square2017

    • Author(s)
      Suzuki Yuta
    • Journal Title

      Functiones et Approximatio Commentarii Mathematici

      Volume: 57 Issue: 1 Pages: 61-76

    • DOI

      10.7169/facm/1616

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A mean value of the representation function for the sum of two primes in arithmetic progressions2017

    • Author(s)
      Suzuki Yuta
    • Journal Title

      International Journal of Number Theory

      Volume: 13 Issue: 04 Pages: 977-990

    • DOI

      10.1142/s1793042117500518

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Presentation] On error term estimates a la Walfisz for mean values of arithmetic functions2018

    • Author(s)
      鈴木雄太
    • Organizer
      International Conference on Number Theory dedicated to the 70th birthdays of Professors Antanas Laurincikas and Eugenijus Manstavicius
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On error term estimates a la Walfisz for mean values of arithmetic functions2018

    • Author(s)
      鈴木雄太
    • Organizer
      Analytic Number Theory and Related Topics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 素数に関連したLambert級数の無理性について2018

    • Author(s)
      鈴木雄太
    • Organizer
      Functional Equations and Transcendence
    • Related Report
      2018 Annual Research Report
  • [Presentation] On error term estimates a la Walfisz for mean values of arithmetic functions2018

    • Author(s)
      鈴木雄太
    • Organizer
      解析数論セミナー
    • Related Report
      2018 Annual Research Report
  • [Presentation] On the Fujii-type explicit formula for the sum of two primes in arithmetic progressions (joint work with G. Bhowmik, K. Halupczok, and K. Matsumoto)2018

    • Author(s)
      鈴木雄太
    • Organizer
      解析数論セミナー
    • Related Report
      2018 Annual Research Report
  • [Presentation] On error term estimates a la Walfisz for mean values of arithmetic functions2018

    • Author(s)
      鈴木雄太
    • Organizer
      Shandong University Number Theory Seminar
    • Related Report
      2018 Annual Research Report
  • [Presentation] On binary additive problems with prime variables in short intervals2018

    • Author(s)
      鈴木雄太
    • Organizer
      Participative learning seminar analytic number theory
    • Related Report
      2018 Annual Research Report
  • [Presentation] On binary additive problems with prime variables in short intervals2018

    • Author(s)
      鈴木雄太
    • Organizer
      Johannes Kepler University of Linz Guest Lecture
    • Related Report
      2018 Annual Research Report
  • [Presentation] On relatively prime amicable pairs2018

    • Author(s)
      鈴木雄太
    • Organizer
      理研数論セミナー特別企画
    • Related Report
      2018 Annual Research Report
  • [Presentation] On relatively prime amicable pairs2018

    • Author(s)
      鈴木雄太
    • Organizer
      解析数論セミナー
    • Related Report
      2017 Annual Research Report
  • [Presentation] 互いに素な友愛数について2018

    • Author(s)
      鈴木雄太
    • Organizer
      第11回 多重ゼータ研究集会 & 第39回 関西多重ゼータ研究会
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] On relatively prime amicable pairs2018

    • Author(s)
      鈴木雄太
    • Organizer
      Diophantine Analysis and Related Fields 2018
    • Related Report
      2017 Annual Research Report
  • [Presentation] 互いに素な友愛数について2018

    • Author(s)
      鈴木雄太
    • Organizer
      2018早稲田整数論研究集会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 互いに素な友愛数について2018

    • Author(s)
      鈴木雄太
    • Organizer
      日本数学会2018年度年会
    • Related Report
      2017 Annual Research Report
  • [Presentation] The Graph Ramsey Number $R(F_l,K_6)$2017

    • Author(s)
      鈴木雄太
    • Organizer
      Combinatoire et Theorie des Nombres
    • Related Report
      2017 Annual Research Report
  • [Presentation] On prime vs. prime power pairs2017

    • Author(s)
      鈴木雄太
    • Organizer
      Arithmetique en Plat Pays : Journee printaniere
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On the sum of a prime and a square in short intervals2017

    • Author(s)
      鈴木雄太
    • Organizer
      神戸整数論集会2017
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] On a set of souvenirs in small travel bags2017

    • Author(s)
      鈴木雄太
    • Organizer
      解析数論セミナー
    • Related Report
      2017 Annual Research Report
  • [Presentation] 素数の解体ショー2017

    • Author(s)
      鈴木雄太
    • Organizer
      近畿大学数学講演会
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] On the sum of a prime and a square in short intervals2017

    • Author(s)
      鈴木雄太
    • Organizer
      NUMBER THEORY WEEK 2017: A conference on the occasion of the 60th birthday of Jerzy Kaczorowski
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On the sum of a prime and a square in short intervals2017

    • Author(s)
      鈴木雄太
    • Organizer
      解析的整数論とその周辺
    • Related Report
      2017 Annual Research Report
  • [Presentation] 素数と平方数の和について2017

    • Author(s)
      鈴木雄太
    • Organizer
      第 13 回数学総合若手研究集会
    • Place of Presentation
      北海道大学
    • Related Report
      2016 Annual Research Report
  • [Presentation] On the sum of a prime and a square in short intervals2017

    • Author(s)
      鈴木雄太
    • Organizer
      French-Japanese Zeta Functions
    • Place of Presentation
      Lille, France
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 素数と素数べきの組について2016

    • Author(s)
      鈴木雄太
    • Organizer
      解析数論セミナー
    • Place of Presentation
      名古屋大学多元数理科学研究科
    • Related Report
      2016 Annual Research Report
  • [Presentation] 素数 vs. 素数べき2016

    • Author(s)
      鈴木雄太
    • Organizer
      愛媛大学代数セミナー
    • Place of Presentation
      愛媛大学
    • Related Report
      2016 Annual Research Report
  • [Presentation] On prime vs. prime power pairs2016

    • Author(s)
      鈴木雄太
    • Organizer
      The Sixth International Conference Analytic and Probabilistic Methods in Number Theory
    • Place of Presentation
      Palanga, Lithuania
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On prime vs. prime power pairs2016

    • Author(s)
      鈴木雄太
    • Organizer
      解析的整数論の諸問題と展望
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2016 Annual Research Report
  • [Presentation] The Graph Ramsey Number R(F_l,K_6) (joint work with Shin-ya Kadota and Tomokazu Onozuka)2016

    • Author(s)
      鈴木雄太
    • Organizer
      解析数論セミナー
    • Place of Presentation
      名古屋大学多元数理科学研究科
    • Related Report
      2016 Annual Research Report

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Published: 2016-05-17   Modified: 2024-03-26  

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