منابع مشابه
The spectral decomposition of shifted convolution sums
Let π1, π2 be cuspidal automorphic representations of PGL2(R) of conductor 1 and Hecke eigenvalues λπ1,2 (n), and let h > 0 be an integer. For any smooth compactly supported weight functions W1,2 : R → C and any Y > 0 a spectral decomposition of the shifted convolution sum
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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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We present a monotonic convolution for planar regions A and B bounded by line and circular arc segments. The Minkowski sum equals the union of the cells with positive crossing numbers in the arrangement of the convolution, as is the case for the kinetic convolution. The monotonic crossing number is bounded by the kinetic crossing number, and also by the maximum number of intersecting pairs of m...
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In a recent important paper, Hoffstein and Hulse [14] generalized the notion of Rankin-Selberg convolution L-functions by defining shifted convolution L-functions. We investigate symmetrized versions of their functions, and we prove that the generating functions of certain special values are linear combinations of weakly holomorphic quasimodular forms and “mixed mock modular” forms.
متن کاملAsymptotic bounds for special values of shifted convolution Dirichlet series
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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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2013
ISSN: 0012-7094
DOI: 10.1215/00127094-2371416