Multiplicative functions over short segments
Nonlinear exponential twists of the Liouville function
Let λ(n) be the Liouville function. We find a nontrivial upper bound for the sum The main tool we use is Vaughan’s identity for λ(n).
Nonvanishing of Fourier coefficients of newforms in progressions
Numbers with a large prime factor
O zakonomernostyakh upravlyayushchikh khaotichnostyu povedeniya funkcii i ee proizvodnyh
On a fundamental result in van der Corput's method of estimating exponential sums
On a multiplicative hybrid problem
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 an Effective Order Estimate of the Riemann Zeta Function in the Critical Strip.
On an estimate by Weyl and Vinogradov.
On an exponential sum.
On certain arithmetic functions involving the greatest common divisor
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.
On Certain Divisor Functions in Short Intervals
On exponential sums over smooth numbers.
On exponential sums with multiplicative coefficients, II
On Hecke eigenvalues at primes of the form [g(n)]
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)].
On -free numbers over Beatty sequences
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 ...
On lattice points in large convex bodies
On Linnik's approximation to Goldbach's problem, I