The Reciprocity Law for the Second Moment of Automorphic L-functions
نویسنده
چکیده
where A and B are some explicit constants. This provides an asymptotic formula for M(p, q) − √ p/qM(−q, p) under the condition that p ≪ q2/3−ε. The error term above was improved by Young [6] so that the asymptotic formula holds for p ≪ q1−ε. In this paper, we consider the twisted moments of the families of L-functions arising from S∗ 2 (p) and S∗ 2 (q), the sets of primitive Hecke eigenforms of weight 2, level p and q respectively (p, q prime). For f(z) ∈ S∗ 2 (q), f has a Fourier expansion
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تاریخ انتشار 2009