Reference : Splitting fields of X^n-X-1 and modular forms
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Splitting fields of X^n-X-1 and modular forms
Wiese, Gabor mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Hong Kong University Number Theory Days 2022
21/7/2022 - 25/7/2022
Hong Kong (online)
[en] In his article `On a theorem of Jordan', Serre considered the family of polynomials f_n(X) = X^n-X-1 and the counting function of the number of roots of f_n over the finite field F_p, seen as function in p. He explicitly showed the `modularity' of this function for n=3,4.
In this talk, I report on joint work with Alfio Fabio La Rosa and Chandrashekhar Khare, in which we treat the case n=5 in several different ways.

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