Back to Search
Start Over
A conjecture of Gross and Zagier: Case E(ℚ)tor≅ℤ/3ℤ.
- Source :
-
International Journal of Number Theory . Oct2019, Vol. 15 Issue 9, p1793-1800. 8p. - Publication Year :
- 2019
-
Abstract
- 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 , P K the Heegner point in E (K) , and III (E / K) the Shafarevich–Tate group of E over K. Let 2 u K be the number of roots of unity contained in K. Gross and Zagier conjectured that if P K has infinite order in E (K) , then the integer c ⋅ m ⋅ u K ⋅ | III (E / K) | 1 2 is divisible by | E (ℚ) tor |. In this paper, we show that this conjecture is true if E (ℚ) tor ≅ ℤ / 3 ℤ. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 17930421
- Volume :
- 15
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- International Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 138934009
- Full Text :
- https://doi.org/10.1142/S1793042119501008