Tate-Shafarevich Groups and Frobenius Fields of Reductions of Elliptic Curves
| dc.creator | Shparlinski, Igor E. | |
| dc.date | 2007-07-19 | |
| dc.date | 2007-11-29 | |
| dc.date.accessioned | 2026-07-07T08:45:32Z | |
| dc.date.available | 2026-07-07T08:45:32Z | |
| dc.description | Let $\E/\Q$ be a fixed elliptic curve over $\Q$ which does not have complex multiplication. Assuming the Generalized Riemann Hypothesis, A. C. Cojocaru and W. Duke have obtained an asymptotic formula for the number of primes $p\le x$ such that the reduction of $\E$ modulo p has a trivial Tate-Shafarevich group. Recent results of A. C. Cojocaru and C. David lead to a better error term. We introduce a new argument in the scheme of the proof which gives further improvement. | |
| dc.identifier | https://arxiv.org/abs/0707.2976 | |
| dc.identifier | http://arxiv.org/abs/0707.2976 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142991 | |
| dc.subject | Number Theory | |
| dc.subject | 11G07, 11N35, 11L40, 14H52 | |
| dc.title | Tate-Shafarevich Groups and Frobenius Fields of Reductions of Elliptic Curves | |
| dc.type | text |