Results 11 to 20 of about 51,880 (308)
The spectral decomposition of shifted convolution sums [PDF]
Duke Mathematical Journal, 2008 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 ...
Valentin Blomer, Gergely Harcos
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Bernoulli Identities and Combinatoric Convolution Sums with Odd Divisor Functions [PDF]
Abstract and Applied Analysis, 2014 We study the combinatoric convolution sums involving odd divisor functions, their relations to Bernoulli numbers, and some interesting applications.
Daeyeoul Kim, Yoon Kyung Park
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Convolution formula for the sums of generalized Dirichlet $L$-functions [PDF]
, 2019 Using the Kuznetsov trace formula, we prove a spectral decomposition for the sums of generalized Dirichlet $L$-functions. Among applications are an explicit formula relating norms of prime geodesics to moments of symmetric square $L$-functions and an ...
Olga Balkanova, Dmitry Frolenkov
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Convolution identities for divisor sums and modular forms. [PDF]
Proc Natl Acad Sci U S AWe consider certain convolution sums that are the subject of a conjecture by Chester, Green, Pufu, Wang, and Wen in string theory. We prove a generalized form of their conjecture, explicitly evaluating absolutely convergent sums ∑
Fedosova K +2 more
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Evaluation of the convolution sums ∑al+bm=n lσ(l) σ(m) with ab ≤ 9
Open Mathematics, 2017 The generating functions of divisor functions are quasimodular forms of weight 2 and their products belong to a space of quasimodular forms of higher weight.
Park Yoon Kyung
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Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8
Open MathematicsIn this article, we compute binomial convolution sums of divisor functions associated with the Dirichlet character modulo 8, which is the remaining primitive Dirichlet character modulo powers of 2 yet to be considered.
Jin Seokho, Park Ho
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CONVOLUTION SUMS INVOLVING THE DIVISOR FUNCTION [PDF]
Proceedings of the Edinburgh Mathematical Society, 2004 AbstractThe series\begin{alignat*}{2} L_{r,4}(q)\amp=\sum_{n=0}^\infty\sigma(4n+r)q^{4n+r},\amp\quad r\amp=0,1,2,3, \\ M_{r,4}(q)\amp=\sum_{n=0}^\infty\sigma_3(4n+r)q^{4n+r},\amp\quad r\amp=0,1,2,3, \\ N_{r,4}(q)\amp=\sum_{n=0}^\infty\sigma_5(4n+r)q^{4n+r},\amp\quad r\amp=0,1,2,3, \end{alignat*}are evaluated and used to prove convolution formulae such ...
Nathalie Cheng, Kenneth S. Williams
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Bounds on shifted convolution sums for Hecke eigenforms [PDF]
Research in Number Theory, 2022 AbstractShifted convolution sums play a prominent rôle in analytic number theory. Here these sums are considered in the context of holomorphic Hecke eigenforms. We investigate pointwise bounds, mean-square bounds consistent with the optimal conjectural bound, and find asymptotics on average for their variance.
Asbjørn Christian Nordentoft +2 more
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A Sieve Method for Shifted Convolution Sums [PDF]
Duke Mathematical Journal, 2022 To appear in Duke Math. J.
Roman Holowinsky
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Convolutions of Continuous Measures and Sums of an Independent Set [PDF]
Proceedings of the American Mathematical Society, 1974 Let E E be a compact independent subset of an l.c.a. group G ; μ 1 , ⋯ , μ n + 1 G;{\mu _1}, \cdots ,{\mu _{n + 1}} continuous ...
James Michael Rago
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