BROWSE

Related Scientist

Researcher

김태경
기하학 수리물리 연구단
more info

A conjecture of Gross and Zagier: Case e (Q) tor ≅ Z&/3Z

Cited 0 time in webofscience Cited 0 time in scopus
25 Viewed 6 Downloaded
Title
A conjecture of Gross and Zagier: Case e (Q) tor ≅ Z&/3Z
Author(s)
Byeon D.; Taekyung Kim; Yhee D.
Publication Date
2019-10
Journal
INTERNATIONAL JOURNAL OF NUMBER THEORY, v.15, no.09, pp.1793 - 1800
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Abstract
© 2019 World Scientific Publishing Company.Let E be an elliptic curve defined over Q of conductor N, c the Manin constant of E, and m the product of Tamagawa numbers of E at prime divisors of N. Let K be an imaginary quadratic field where all prime divisors of N split in K, PK the Heegner point in E(K), and III(E/K) the Shafarevich-Tate group of E over K. Let 2uK be the number of roots of unity contained in K. Gross and Zagier conjectured that if PK has infinite order in E(K), then the integer c m uK |III(E/K)|1 2 is divisible by |E(Q)tor|. In this paper, we show that this conjecture is true if E(Q)torZ/3Z;
URI
https://pr.ibs.re.kr/handle/8788114/6829
ISSN
1793-0421
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > Journal Papers (저널논문)
Files in This Item:
2019_TKK_A conjecture of Gross and Zagier Case E(Q)tor≅Z3Z.pdfDownload

qrcode

  • facebook

    twitter

  • Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.
해당 아이템을 이메일로 공유하기 원하시면 인증을 거치시기 바랍니다.

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Browse