On the application of Turán's method to the theory of Dirichlet L-functions
On the arithmetic of cross-ratios and generalised Mertens’ formulas
We develop the relation between hyperbolic geometry and arithmetic equidistribution problems that arises from the action of arithmetic groups on real hyperbolic spaces, especially in dimension . We prove generalisations of Mertens’ formula for quadratic imaginary number fields and definite quaternion algebras over , counting results of quadratic irrationals with respect to two different natural complexities, and counting results of representations of (algebraic) integers by binary quadratic, Hermitian...
On the arithmetic structure of the integers whose sum of digits is fixed
On the arithmetical functions and .
On the asymmetric divisor problem with congruence conditions
A certain generalized divisor function is studied which counts the number of factorizations of a natural number into integer powers with prescribed exponents under certain congruence restrictions. An -estimate is established for the remainder term in the asymptotic for its Dirichlet summatory function.
On the asymptotic behavior of some counting functions
The investigation of certain counting functions of elements with given factorization properties in the ring of integers of an algebraic number field gives rise to combinatorial problems in the class group. In this paper a constant arising from the investigation of the number of algebraic integers with factorizations of at most k different lengths is investigated. It is shown that this constant is positive if k is greater than 1 and that it is also positive if k equals 1 and the class group satisfies...
On the asymptotic behavior of the Dickman-de Bruijn function.
On the Asymptotic Behaviour of Sums ...g (n) ...x/n...
On the Asymptotic Behaviour of the Ideal Counting Function in Quadratic Number Fields.
On the asymptotic formulae for some functions connected with powers of the zeta function
On the asymptotic formulas for powerful numbers.
On the Average Number of Direct Factors of a Finite Abelian Group.
On the average number of direct factors of a finite abelian group
On the average number of direct factors of a finite Abelian group
On the average number of direct factors of a finite abelian group (“sur les variété abéliennes”)
On the average number of direct factors of finite abelian groups
On the average number of direct factors of finite abelian groups (II)
On the average number of unitary factors of finite abelian groups
On the average number of unitary factors of finite abelian groups
On the average of the sum-of-a-divisors function
We prove an Ω result on the average of the sum of the divisors of n which are relatively coprime to any given integer a. This generalizes the earlier result for a prime proved by Adhikari, Coppola and Mukhopadhyay.