On the set of divisors of an integer.
On the Shanks-Rényi race problem
On the Sign Changes of (...(x) - lix). II.
On the size of prime factors of integers
On the size of the first factor of the class number of a cyclotomic field.
On the sphere problem.
One of the oldest problems in analytic number theory consists of counting points with integer coordinates in the d-dimensional ball. It is very easy to find a main term for the counting function, but the size of the error term is difficult to estimate (...).
On the spinor zeta functions problem: higher power moments of the Riesz mean
Let F be a Siegel cusp form of integral weight k on the Siegel modular group Sp₂(ℤ) of genus 2. The coefficients of the spinor zeta function are denoted by cₙ. Let be the Riesz mean of cₙ. Kohnen and Wang obtained the truncated Voronoï-type formula for under the Ramanujan-Petersson conjecture. In this paper, we study the higher power moments of , and then derive an asymptotic formula for the hth (h=3,4,5) power moments of by using Ivić’s large value arguments and other techniques.
On the square-free sieve
On the sum ... D(n) ... (n + N).
On the sum of iterations of the Euler function.
On the sum of the first n values of the Euler function
Let ϕ(n) be the Euler function of n. We put and give an asymptotic formula for the second moment of E(n).
On the sum of the number of divisors in a short segment
On the Sum-of-Divisors Function of the Numbers of Fermat and Ferentinou-Nicolacopoulou
On the switching principle in sieve theory.
On the symmetry of divisor sums functions in almost all short intervals.
On the symmetry of square-free supported arithmetical functions in short intervals.
On the symmetry of the divisor function in almost all short intervals
On the tails of the limiting distribution function of the error term in the Dirichlet divisor problem
On the Tauberian constant in the Ikehara theorem
On the ternary Goldbach problem with primes in arithmetic progressions having a common modulus
For and any sufficiently large odd we show that for almost all there exists a representation with primes mod for almost all admissible triplets of reduced residues mod .