On the Error Term for the Counting Functions of Finite Abelian Groups.
On the maximal order in and
On the method of exponent pairs
On the moderate growth of generalized Dirichlet series for hypoelliptic polynomials
On the number of Abelian groups of a given number.
On the number of abelian groups of a given order
On the number of abelian groups of a given order (supplement)
1. Introduction. The aim of this paper is to supply a still better result for the problem considered in [2]. Let A(x) denote the number of distinct abelian groups (up to isomorphism) of orders not exceeding x. We shall prove Theorem 1. For any ε > 0, , where C₁, C₂ and C₃ are constants given on page 261 of [2]. Note that 50/199=0.25125..., thus improving our previous exponent 40/159=0.25157... obtained in [2]. To prove Theorem 1, we shall proceed along the line of approach presented in [2]....
On the Number of Integral Ideals in Galois Extensions.
On the number of primitive λ-roots
On the number of subgroups of finite abelian groups
Letwhere denotes the number of subgroups of all abelian groups whose order does not exceed and whose rank does not exceed , and is the error term. It is proved that
On the orbits of Singer groups and their subgroups.
On the quantitative unit sum number problem-an application of the subspace theorem
On the value distribution of a class of arithmetic functions
This article deals with the value distribution of multiplicative prime-independent arithmetic functions with if is -free ( a fixed integer), else, and . An asymptotic result is established with an error term probably definitive on the basis of the present knowledge about the zeros of the zeta-function. Applications to the enumerative functions of Abelian groups and of semisimple rings of given finite order are discussed.
Permutation functions and (n,m)-commutativity of semigroups .
p-Nilpotence, classifying space indecomposability, and other properties of almost all finite groups.
Polynômes de ayant un diviseur de degré donné
Prime geodesic theorem.
Products related to Gauss sums.
Quantitative aspects of non-unique factorization: A general theory with applications to algebraic function fields.
Reducibility of lacunary polynomials, XI