On an almost pure sieve
On an arithmetic function considered by Pillai
For every positive integer let be the largest prime number . Given a positive integer , we study the positive integer such that if we define recursively for , then is a prime or . We obtain upper bounds for as well as an estimate for the set of whose takes on a fixed value .
On an asymmetric divisor problem with congruence conditions.
On an asymptotic formula for the Niven numbers.
On an Asymptotic Formula of Ramanujan.
On an asymptotic formula of Srinivasa Ramanujan
On an average of primes in short intervals
On an estimate of Walfisz and Saltykov for an error term related to the Euler function
The technique developed by A. Walfisz in order to prove (in 1962) the estimate for the error term related to the Euler function is extended. Moreover, the argument is simplified by exploiting works of A.I. Saltykov and of A.A. Karatsuba. It is noted in passing that the proof proposed by Saltykov in 1960 of is erroneous and once corrected “only” yields Walfisz’ result. The generalizations obtained can be applied to error terms related to various classical - and less classical - arithmetical...
On another sieve method and the numbers that are a sum of two hth powers: II.
On arithmetic progressions having only few different prime factors in comparison with their length
On Artin's conjecture.
On Artin's Conjecture and Euclid's Algorithm in Global Fields.
On asymptotically correlated -multiplicative functions.
On Binary Equations.
On Bombieri's asymptotic sieve
On Bourgain's bound for short exponential sums and squarefree numbers
We use Bourgain's recent bound for short exponential sums to prove certain independence results related to the distribution of squarefree numbers in arithmetic progressions.
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 certain functions that generalize von Mangoldt’s function
On certain form and its Rankin-Selberg convolution
We consider to be the -function attached to a particular automorphic form on . We establish an upper bound for the mean square estimate on the critical line of Rankin-Selberg -function . As an application of this result, we give an asymptotic formula for the discrete sum of coefficients of .