573 research outputs found
Period integrals and Rankin-Selberg L-functions on GL(n)
We compute the second moment of a certain family of Rankin-Selberg
-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
Review of Alison Dyer\u27s I’d Write the Sea Like a Parlour Game
The spectral decomposition of shifted convolution sums
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
For Dirichlet series roughly of the type
the subconvexity bound is proved on
the critical lines . 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 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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