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math.NT2012★ 3 cited
Evaluating modular forms on Shimura curves
Paul D. Nelson
Let f be a newform, as specified by its Hecke eigenvalues, on a Shimura curve X. We describe a method for evaluating f. The most interesting case is when X arises as a compact quot…
math.NT2012★ 1 cited
Bounds for Rankin--Selberg integrals and quantum unique ergodicity for powerful levels
Paul D. Nelson, Ameya Pitale, Abhishek Saha
Let f be a classical holomorphic newform of level q and even weight k. We show that the pushforward to the full level modular curve of the mass of f equidistributes as qk -> infini…
math.NT2012
Stable averages of central values of Rankin-Selberg L-functions: some new variants
Paul D. Nelson
As shown by Michel-Ramakrishan (2007) and later generalized by Feigon-Whitehouse (2008), there are "stable" formulas for the average central L-value of the Rankin-Selberg convoluti…