573 research outputs found

    Period integrals and Rankin-Selberg L-functions on GL(n)

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    We compute the second moment of a certain family of Rankin-Selberg LL-functions L(f x g, 1/2) where f and g are Hecke-Maass cusp forms on GL(n). Our bound is as strong as the Lindel\"of hypothesis on average, and recovers individually the convexity bound. This result is new even in the classical case n=2.Comment: accepted version with minor change

    I\u27d Write the Sea Like a Parlour Game by Alison Dyer

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    Review of Alison Dyer\u27s I’d Write the Sea Like a Parlour Game

    The spectral decomposition of shifted convolution sums

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    We obtain a spectral decomposition of shifted convolution sums in Hecke eigenvalues of holomorphic or Maass cusp forms.Comment: 15 pages, LaTeX2e; v2: corrected and slightly expanded versio

    Subconvexity for a double Dirichlet series

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    For Dirichlet series roughly of the type Z(s,w)=sumdL(s,chid)d−wZ(s, w) = sum_d L(s, chi_d) d^{-w} the subconvexity bound Z(s,w)≪(sw(s+w))1/6+εZ(s, w) \ll (sw(s+w))^{1/6+\varepsilon} is proved on the critical lines ℜs=ℜw=1/2\Re s = \Re w = 1/2. The convexity bound would replace 1/6 with 1/4. In addition, a mean square bound is proved that is consistent with the Lindel\"of hypothesis. An interesting specialization is s=1/2s=1/2 in which case the above result give a subconvex bound for a Dirichlet series without an Euler product.Comment: 17 page
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