대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제58권1호
  • /
  • Pages.163-170
  • /
  • 2021
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

A PROOF OF THE CONJECTURE OF MAZUR-RUBIN-STEIN

  • Sun, Hae-Sang (Ulsan National Institute of Science and Technology)
  • 투고 : 2020.02.19
  • 심사 : 2020.03.25
  • 발행 : 2021.01.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We present a concise proof of the conjecture of Mazur-Rubin-Stein on the distribution of modular symbols.

키워드

참고문헌

  1. V. Blomer, E. Fouvry, E. Kowalski, P. Michel, D. Milicevic, and W. Sawin, The second moment theory of families of L-functions, to appear in Memoirs of the AMS.
  2. N. Diamantis, J. Hoffstein, E. M. Kiral, and M. Lee, Additive twists and a conjecture by Mazur, Rubin and Stein, J. Number Theory 209 (2020), 1-36. https://doi.org/10.1016/j.jnt.2019.11.016
  3. D. R. Heath-Brown, Arithmetic applications of Kloosterman sums, Nieuw Arch. Wiskd. (5) 1 (2000), no. 4, 38084.
  4. M. Kim and H.-S. Sun, Modular symbols and modular L-values with cyclotomic twists, submitted.
  5. J. Lee and H.-S. Sun, Dynamics of continued fractions and distribution of modular symbols, submitted.
  6. B. Mazur, Relatively few rational points, Lecture note at Cal Tech.
  7. Y. N. Petridis and M. S. Risager, Arithmetic statistics of modular symbols, Invent. Math. 212 (2018), no. 3, 997-1053. https://doi.org/10.1007/s00222-017-0784-7