E-viri
Recenzirano
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Ma, Q.
Acta mathematica Hungarica, 12/2022, Letnik: 168, Številka: 2Journal Article
Let Λ π ( n ) denote the n th coefficient in the Dirichlet series expansion of the logarithmic derivative of L ( s , π ) associated with an automorphic irreducible cuspidal representation of GL m over Q . In this paper, for all α of irrational type 1 lying in the interval 0 , 1 , we investigate the best possible estimate for the sum ∑ n ≤ x Λ π ( n ) e ( n α ) under a certain assumption. And we consider the metric result on the exponential sum involving automorphic L -functions without any assumptions. Let Λ ( n ) be the von Mangoldt function. Then as an application, for ε > 0 and all 0 < α < 1 in a set of full Lebesgue measure (depending on π ), we obtain ∑ n ≤ x Λ ( n ) λ π ( n ) e ( n α ) = O ( x 5 6 + ε ) .
