$p$-adic properties of modular shifted convolution Dirichlet series
نویسندگان
چکیده
منابع مشابه
p-ADIC PROPERTIES OF MODULAR SHIFTED CONVOLUTION DIRICHLET SERIES
Ho stein and Hulse recently introduced the notion of shifted convolution Dirichlet series for pairs of modular forms f1 and f2. The second two authors investigated certain special values of symmetrized sums of such functions, numbers which are generally expected to be mysterious transcendental numbers. They proved that the generating functions of these values in the h-aspect are linear combinat...
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In [15], Hoffstein and Hulse defined the shifted convolution series of two cusp forms by “shifting” the usual Rankin-Selberg convolution L-series by a parameter h. We use the theory of harmonic Maass forms to study the behavior in h-aspect of certain values of these series and prove a polynomial bound as h → ∞. Our method relies on a result of Mertens and Ono [22], who showed that these values ...
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Let f be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus and denote by λf (n) its n-th Hecke eigenvalue. Let r(n) = # { (n1, n2) ∈ Z : n21 + n22 = n } . In this paper, we study the shifted convolution sum Sh(X) = ∑ n≤X λf (n+ h)r(n), 1 ≤ h ≤ X, and establish uniform bounds with respect to the shift h for Sh(X).
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2015
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/12809