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Bounds on special values of L-functions of elliptic curves in an Artin-Schreier family. (arXiv:1801.08492v1 [math.NT])
来源于:arXiv
In this paper, we study a certain Artin--Schreier family of elliptic curves
over the function field $\mathbb{F}_q(t)$. We prove an asymptotic estimate on
the size of the special value of their $L$-function in terms of the degree of
their conductor; loosely speaking, we show that the special values are
"asymptotically as large as possible".
We also provide an explicit expression for the $L$-function of the elliptic
curves in the family. The proof of the main result uses this expression and a
detailed study of the distribution of some character sums related to
Kloosterman sums. Via the BSD conjecture, the main result translates into an
analogue of the Brauer--Siegel theorem for these elliptic curves. 查看全文>>