Year: 2025
Type: article
Abstract: Given an elliptic curve $ E $ over $ \mathbb {Q} $ of analytic rank zero, its L-function can be twisted by an even primitive Dirichlet character $ \chi $ of order $ q $ , and in many cases its associated special L-value $ \mathscr {L}(E, \chi ) $ is known to be integral after normalizing by certain periods. This article determines the precise value of $ \mathscr {L}(E, \chi ) $ in terms of Birch–Swinnerton-Dyer invariants when $ q = 3 $ , classifies their asymptotic densities modulo $ 3 $ by fixing $ E $ and varying $ \chi $ , and presents a lower bound on the $ 3 $ -adic valuation of $ \mathscr {L}(E, 1) $ , all of which arise from a congruence of modular symbols. These results also explain some phenomena observed by Dokchitser–Evans–Wiersema and by Kisilevsky–Nam.
Source: Canadian Journal of Mathematics
Author: David Kurniadi Angdinata
Institution: University of London
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4411501032