On the maximum row and column sum norm of GCD and related matrices.
On the mean square of the divisor function in short intervals
We provide upper bounds for the mean square integralwhere and lies in a suitable range. For a fixed integer, is the error term in the asymptotic formula for the summatory function of the divisor function , generated by .
On the Mean Square of the Riemann Zeta Function and the Divisor Problem
ON THE MEAN SQUARE OF THE RIEMANN ZETA-FUNCTION IN SHORT INTERVALS
On the mean square of the zeta-function and the divisor problem.
On the mean value of the index of composition of an integer
On the mean value of the remainder term of the prime number formula
On the method of exponent pairs
On the Möbius function.
On the Möbius sum function
On the moderate growth of generalized Dirichlet series for hypoelliptic polynomials
On the moments of the Carmichael λ function
On the Multiplicative Group Generated by a Dense Sequence of Integers.
On the non-linear sieve
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
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 coprime integer pairs within a circle
On the number of distinct values of Euler's φ-function