The number of coefficients of automorphic L-functions for GL m of same signs

Abstract : Let π be an irreducible unitary cuspidal representation for GL m (A Q), and let L(s, π) be the automorphic L-function attached to π, which has a Dirich-let series expression in the half-plane Re s > 1. When π is self-contragredient, all the coefficients in the Dirichlet series expression are real. In this paper we give non-trivial lower bounds for the number of positive and negative coefficients, respectively .
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Jianya Liu, Jie Wu. The number of coefficients of automorphic L-functions for GL m of same signs. Journal of Number Theory, Elsevier, 2015, 148, pp.429-450. ⟨10.1016/j.jnt.2014.09.020⟩. ⟨hal-01278944⟩

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