O součtech Gaussových
O zakonomernostyakh upravlyayushchikh khaotichnostyu povedeniya funkcii i ee proizvodnyh
On a certain class of exponential sums.
On a comparison of Gauss sums with products of Lagrange resolvents
On a congruence relation between Jacobi sums and cyclotomic units.
On a Conjecture of Littlewood Concerning Exponential Sums, I
On a Conjecture of Littlewood Concerning Exponentials Sums, II
On a conjecture of Norton
On a conjecture of Yiming Long
On a fundamental result in van der Corput's method of estimating exponential sums
On a multiple trigonometric series
On a multiplicative hybrid problem
On a Problem Connected with Zeros of ... (s) on the Critical Line.
On a problem of Diophantus
On a product of sines
On a product related to the cubic Gauss sum.
On a question of A. Schinzel: Omega estimates for a special type of arithmetic functions
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.
On a sum involving the integral part function
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).
On a sum involving the Möbius function
Let be the Ramanujan sum, i.e. , where μ is the Möbius function. In a paper of Chan and Kumchev (2012), asymptotic formulas for (k = 1,2) are obtained. As an analogous problem, we evaluate (k = 1,2), where .
On a sum of Vinogradov