Variations of Lehmer's Conjecture for Ramanujan's tau-function

JOURNAL OF NUMBER THEORY

卷:237

Article

Balakrishnan, Jennifer S.¹  Craig, William²  Ono, Ken² 

[1] Boston Univ, Dept Math & Stat, Boston, MA 02215 USA

[2] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA

关键词: Lehmer's Conjecture;   

DOI  :  10.1016/j.jnt.2020.04.009

来源: Elsevier

【 摘 要 】

This result is an example of general theorems (see Theorems 1.2 and 1.3 of [2]) for newforms with trivial mod 2 residual Galois representation. Ramanujan's well-known congruences for tau(n) allow for the simplified proof in these special cases. We make use of the theory of Lucas sequences, the Chabauty- Coleman method for hyperelliptic curves, and facts about certain Thue equations. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free