O zakonomernostyakh upravlyayushchikh khaotichnostyu povedeniya funkcii i ee proizvodnyh
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Ján Mozer (1994)
Czechoslovak Mathematical Journal
Hong-Quan Liu (1999)
Acta Arithmetica
Wen-Guang Zhai (1995)
Acta Arithmetica
Manfred Kühleitner, Werner Nowak (2013)
Open Mathematics
The paper deals with lower bounds for the remainder term in asymptotics for a certain class of arithmetic functions. Typically, these are generated by a Dirichlet series of the form ζ 2(s)ζ(2s−1)ζ M(2s)H(s), where M is an arbitrary integer and H(s) has an Euler product which converges absolutely for R s > σ0, with some fixed σ0 < 1/2.
Bo Chen (2024)
Czechoslovak Mathematical Journal
Let be the integral part of a real number , and let be the arithmetic function satisfying some simple condition. We establish a new asymptotical formula for the sum , which improves the recent result of J. Stucky (2022).
K.M. Bartz (1990)
Monatshefte für Mathematik
Allakov, I.A. (2002)
Sibirskij Matematicheskij Zhurnal
Ding, Ping (2005)
Journal of Mathematical Sciences (New York)
Ekkehard Krätzel, Werner Nowak, László Tóth (2012)
Open Mathematics
The paper deals with asymptotics for a class of arithmetic functions which describe the value distribution of the greatest-common-divisor function. Typically, they are generated by a Dirichlet series whose analytic behavior is determined by the factor ζ2(s)ζ(2s − 1). Furthermore, multivariate generalizations are considered.
Aleksandar Ivić (1994)
Publications de l'Institut Mathématique
Trevor D. Wooley (1997)
Journal für die reine und angewandte Mathematik
Gennady Bachman (2003)
Acta Arithmetica
Stephan Baier, Liangyi Zhao (2013)
Acta Arithmetica
We study the average of the Fourier coefficients of a holomorphic cusp form for the full modular group at primes of the form [g(n)].
Wei Zhang (2023)
Czechoslovak Mathematical Journal
We consider -free numbers over Beatty sequences. New results are given. In particular, for a fixed irrational number of finite type and any constant , we can show that where is the set of positive -free integers and the implied constant depends only on ...
Jingwei Guo (2012)
Acta Arithmetica
J. Pintz, I. Z. Ruzsa (2003)
Acta Arithmetica
Alessandro Languasco, Alberto Perelli (1994)
Annales de l'institut Fourier
Linnik proved, assuming the Riemann Hypothesis, that for any , the interval contains a number which is the sum of two primes, provided that is sufficiently large. This has subsequently been improved to the same assertion being valid for the smaller gap , the added new ingredient being Selberg’s estimate for the mean-square of primes in short intervals. Here we give another proof of this sharper result which avoids the use of Selberg’s estimate and is therefore more in the spirit of Linnik’s...
R. Nair (1993)
Studia Mathematica
Hong-Quan Liu (1994)
Acta Arithmetica
Mei-Chu Chang (2006)
Journal of the European Mathematical Society
The purpose of this paper is to investigate efficient representations of the residue classes modulo , by performing sum and product set operations starting from a given subset of . We consider the case of very small sets and composite for which not much seemed known (nontrivial results were recently obtained when is prime or when log ). Roughly speaking we show that all residue classes are obtained from a -fold sum of an -fold product set of , where and , provided the residue sets...
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