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The spectral decomposition of shifted convolution sums [PDF]
Duke Mathematical Journal, 2008 15 pages, LaTeX2e; v2: corrected and slightly expanded ...
Valentin Blomer, Gergely Harcos
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Bounds on shifted convolution sums for Hecke eigenforms [PDF]
Research in Number Theory, 2021 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
semanticscholar +8 more sources
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
europepmc +5 more sources
Eisenstein series and convolution sums [PDF]
The Ramanujan Journal, 2018 We compute Fourier series expansions of weight $2$ and weight $4$ Eisenstein series at various cusps. Then we use results of these computations to give formulas for the convolution sums $ \sum_{a+p b=n} (a) (b)$, $ \sum_{p_1a+p_2 b=n} (a) (b)$ and $ \sum_{a+p_1 p_2 b=n} (a) (b)$ where $p, p_1, p_2$ are primes.
Zafer Selcuk Aygin
semanticscholar +7 more sources
Arithmetic convolution sums derived from eta quotients related to divisors of 6 [PDF]
Open Mathematics, 2022 The aim of this paper is to find arithmetic convolution sums of some restricted divisor functions. When divisors of a certain natural number satisfy a suitable condition for modulo 12, those restricted divisor functions are expressed by the coefficients ...
Ikikardes Nazli Yildiz +2 more
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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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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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A Sieve Method for Shifted Convolution Sums [PDF]
Duke Mathematical Journal, 2008 To appear in Duke Math. J.
Roman Holowinsky
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Convolution Sums of Some Functions on Divisors [PDF]
Rocky Mountain Journal of Mathematics, 2007 This is an old paper uploaded for archival ...
Heekyoung Hahn
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British Journal of Mathematics & Computer Science, 2014 . The article focuses on the evaluation of convolution sums W k ( n ) := (cid:2) m < nk σ( m )σ( n − km ) involving the sum of divisor function σ( n ) for k = 21, 33, and 35. In this article, our aim is to obtain certain Eisenstein series of level 21 and
Aeran Kim
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