Abstract
Let π be an irreducible unitary cuspidal representation of \(GL_m \left( {\mathbb{A}_\mathbb{Q} } \right)\), m ≥ 2. Assume that π is self-contragredient. The author gets upper and lower bounds of the same order for fractional moments of automorphic L-function L(s, π) on the critical line under Generalized Ramanujan Conjecture; the upper bound being conditionally subject to the truth of Generalized Riemann Hypothesis.
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Project supported by the National Natural Science Foundation of China (No. 10971119).
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Pi, Q. Fractional moments of automorphic L-functions on GL(m). Chin. Ann. Math. Ser. B 32, 631–642 (2011). https://doi.org/10.1007/s11401-011-0650-7
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DOI: https://doi.org/10.1007/s11401-011-0650-7