Journal ArticleDOI
The divisor problem for d 4 ( n ) in short intervals
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In this paper, the authors established an asymptotic formula for the sum of the sum √ √ x < n \leqq x + y √ 1/2 log x when y is large compared to x.Abstract:
In this paper we establish an asymptotic formula for the sum
$$ {\sum\limits_{x < n \leqq x + y} {d_{4} (n)} } $$
when y is large compared to x
1/2 log x.read more
Citations
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Journal ArticleDOI
Square-root cancellation for sums of factorization functions over short intervals in function fields
TL;DR: In this paper, the singular locus of a variety of L-functions whose Fq-points control the sum of the divisor function and other similar arithmetic functions over function fields is calculated.
Journal ArticleDOI
The Selberg-Delange method in short intervals with some applications
TL;DR: In this article, the authors established a quite general mean value result of arithmetic functions over short intervals with the Selberg-Delange method and gave some applications, in particular, they generalize Selberg's result on the distribution of integers with a given number of prime factors and Deshouillers-Dress-Tenenbaum's arcsin law on divisors to the short interval case.
Posted Content
Square-root cancellation for sums of factorization functions over short intervals in function fields
TL;DR: In this article, the singular locus of a variety of functions whose points control the sum was calculated by a geometric method, inspired by the work of Hast and Matei, where they calculated the singular location of a function whose points controlled the sum.
Journal ArticleDOI
Short interval asymptotics for a class of arithmetic functions
TL;DR: In this paper, a general asymptotic formula for sums of two squares was proposed, which permits applications to sums like sum of divisors, sums of squares, etc.
Journal ArticleDOI
Short interval results for a class of arithmetic functions
TL;DR: Using estimates on Hooley's $\Delta$-function and a short interval version of the celebrated Dirichlet hyperbola principle, this paper derived an asymptotic formula for a class of arithmetic functions over short segments.
References
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Book
The Theory of the Riemann Zeta-Function
TL;DR: The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it one of the most important tools in the study of prime numbers as mentioned in this paper.
Book
The Riemann Zeta-Function
TL;DR: For Re s = σ > 1, the Riemann zeta function ζ(s) is defined by as discussed by the authors, and it follows from the definition that ζ is an analytic function in the halfplane Re s > 1.
Journal ArticleDOI
Exponential sums and lattice points III
TL;DR: In the case of the Dirichlet divisor problem, the number of points of the integer lattice in a planar domain bounded by a piecewise smooth curve has been shown to be upper bounded by the radius of the maximum radius of curvature as mentioned in this paper.