Displaying similar documents to “New examples of modular rigid Calabi-Yau threefolds.”

Modularity of Galois representations

Chris Skinner (2003)

Journal de théorie des nombres de Bordeaux


This paper is essentially the text of the author’s lecture at the 2001 Journées Arithmétiques. It addresses the problem of identifying in Galois-theoretic terms those two-dimensional, p -adic Galois representations associated to holomorphic Hilbert modular newforms.

Computations of Galois representations associated to modular forms of level one

Peng Tian (2014)

Acta Arithmetica


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...