Sums of higher divisor functions
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DOI: 10.1016/j.jnt.2020.08.009
Abstract: Abstract Let d k ( n ) denote the k-th divisor function. In this paper, we study the asymptotic formula of the sum ∑ 1 ≤ n 1 , n 2 , … , n… read more here.
Keywords: sums higher; divisor functions; higher divisor;
Generalized divisor functions in arithmetic progressions: I
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DOI: 10.1016/j.jnt.2021.03.021
Abstract: Abstract We prove some distribution results for the k-fold divisor function in arithmetic progressions to moduli that exceed the square-root of length X of the sum, with appropriate constrains and averaging on the moduli, saving… read more here.
Keywords: generalized divisor; divisor functions; arithmetic progressions; functions arithmetic ... See more keywords
A PROOF OF MERCA’S CONJECTURES ON SUMS OF ODD DIVISOR FUNCTIONS
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DOI: 10.1017/s0004972721000678
Abstract: Abstract Merca [‘Congruence identities involving sums of odd divisors function’, Proc. Rom. Acad. Ser. A Math. Phys. Tech. Sci. Inf. Sci. 22(2) (2021), 119–125] posed three conjectures on congruences for specific convolutions of a sum… read more here.
Keywords: divisor functions; proof merca; odd divisor; merca conjectures ... See more keywords
On the pairwise maxima of generalised divisor functions
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DOI: 10.1093/qmath/hay008
Abstract: The first author is grateful to the Leverhulme Trust (RPG-2017-320) for the support through the research grant “Moments of L-functions in Function Fields and Random Matrix Theory”. read more here.
Keywords: maxima generalised; pairwise maxima; generalised divisor; divisor functions ... See more keywords
Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8
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DOI: 10.1515/math-2024-0089
Abstract: Abstract In 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. To… read more here.
Keywords: dirichlet character; divisor functions; character modulo; binomial convolution ... See more keywords