Asymptotic formulas. Composite numbers II

Some Asymptotic Formulas in the Theory of Numbers(')

Asymptotic Numbers: II. Order Relation, Infinitesimals and Interval Topology

It lias been shown in 181 that the set of asympototic number~ A is a system of genera­ lized numbers i ncl ndin~ isomorphic;ill y the set of real numbers gt, :1s well as the field of formal power (asymptotic) series. In the present paper, w hich is a contin uation of 181, an order relation i n A is i ntroduced due to A t u roin~ out to be a totally-ordered set. The consis tency between the orde...

Asymptotic formulas for partial sums of class numbers of indefinite binary quadratic forms

Sarnak obtained the asymptotic formula of the sum of the class numbers of indefinite binary quadratic forms from the prime geodesic theorem for the modular group. In the present paper, we show several asymptotic formulas of partial sums of the class numbers by using the prime geodesic theorems for the congruence subgroups of the modular group.

New formulas for Stirling-like numbers and Dobinski-like formulas

Extensions of the Stirling numbers of the second kind and Dobinski-like formulas are proposed in a series of exercises for graduetes. Some of these new formulas recently discovered by me are to be found in A.K.Kwaśniewski’s source paper [1]. These extensions naturally encompass the well known q-extensions.The indicatory references are to point at a part of the vast domain of the foundations of ...

Some Inversion Formulas and Formulas for Stirling Numbers

In the paper we present some new inversion formulas and two new formulas for Stirling numbers.