Conjectures for Moments Associated With Cubic Twists of Elliptic Curves. Issue 1 (2nd January 2023)

• Record Type: Journal Article
• Authors: David, Chantal; Lalín, Matilde; Nam, Jungbae
• Is Part Of: Experimental mathematics. Volume 32:Issue 1(2023)
• Page Start: 105
• Page End: 132
• Publication Date: 2023-01-02
• Subjects: L-functions -- moments -- cubic twists -- random matrix theory; Primary 11M41 -- Secondary 11M50 -- 14G10 -- 11M26; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2021.1926002
• Languages: English
• ISSNs: 1058-6458

Abstract

Abstract: We extend the heuristic introduced by Conrey, Farmer, Keating, Rubinstein, and Snaith in order to formulate conjectures for the ( k, l ) -moments of L -functions of elliptic curves twisted by cubic characters. We also apply the work of Keating and Snaith on the ( k, l ) -moments of characteristic polynomials of unitary matrices to extend our conjecture to k, l ∈ C such that Re ( k ), Re ( l ), and Re ( k + l ) > − 1 . Our conjectures are then numerically tested for two families. A novelty of our conjectures is that cubic twists naturally lead us to consider the possibility k = l .