Variations of Lehmer's Conjecture for Ramanujan's tau-function
نویسندگان
چکیده
We consider natural variants of Lehmer's unresolved conjecture that Ramanujan's tau-function never vanishes. Namely, for n>1 we prove thatτ(n)∉{±1,±3,±5,±7,±691}. This result is an example general theorems (see Theorems 1.2 and 1.3 [2]) newforms with trivial mod 2 residual Galois representation. well-known congruences τ(n) allow the simplified proof in these special cases. make use theory Lucas sequences, Chabauty–Coleman method hyperelliptic curves, facts about certain Thue equations.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2022
ISSN: ['0022-314X', '1096-1658']
DOI: https://doi.org/10.1016/j.jnt.2020.04.009