The Shifted Odd Divisor Functions and Divisor Leaves Model

Shifted convolution and the Titchmarsh divisor problem overFq[t]

Author for correspondence: J. C. Andrade e-mail: [email protected] Shifted convolution and the Titchmarsh divisor problem overFq[t] J. C. Andrade1, L. Bary-Soroker2 and Z. Rudnick2 1Institut des Hautes Études Scientifiques (IHÉS), Le Bois-Marie, 35 Route de Chartres, Bures-sur-Yvette 91440, France 2Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Av...

Shifted convolution and the Titchmarsh divisor problem over 𝔽q[t].

In this paper, we solve a function field analogue of classical problems in analytic number theory, concerning the autocorrelations of divisor functions, in the limit of a large finite field.

Modular Divisor Functions and Quadratic Reciprocity

On the largest prime divisor of an odd harmonic number

A positive integer is called a (Ore’s) harmonic number if its positive divisors have integral harmonic mean. Ore conjectured that every harmonic number greater than 1 is even. If Ore’s conjecture is true, there exist no odd perfect numbers. In this paper, we prove that every odd harmonic number greater than 1 must be divisible by a prime greater than 105.

On the Divisor Products and Proper Divisor Products Sequences*

Let n be a positive integer, Pd(n) denotes the product of all positive divisors of n, qd(n) denotes the product of all proper divisors of n. In this paper, we study the properties of the sequences {PdCn)} and {qd(n)}, and prove that the Makowski &. Schinzel conjecture hold for the sequences {pd(n)} and {qd(n)}.