Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We propose an improved algorithm for computing mod ℓ Galois representations associated to a cusp form f of level one. The proposed method allows us to explicitly compute the case with ℓ = 29 and f of weight k = 16, and the cases with ℓ = 31 and f of weight k = 12,20,22. All the results are rigorously proved to be correct.
As an example, we will compute the values modulo 31 of Ramanujan's tau function at some huge primes up to a sign. Also we will give an improved uper bound on Lehmer's conjecture for Ramanujan's tau function.
As an example, we will compute the values modulo 31 of Ramanujan's tau function at some huge primes up to a sign. Also we will give an improved uper bound on Lehmer's conjecture for Ramanujan's tau function.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
399-411
Opis fizyczny
Daty
wydano
2014
Twórcy
autor
- Department of Mathematics, Nanjing University, 210093, Nanjing, P.R. China
- Dipartimento di Matematica, Università di Roma "Tor Vergata", 00133 Roma, Italy
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-4-5