Shifted convolution and the Titchmarsh divisor problem overFq[t]

Correction to 'Shifted convolution and the Titchmarsh divisor problem over 𝔽q[t]'.

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.

Moments of zeta and correlations of divisor-sums: IV

In this series we examine the calculation of the 2kth moment and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. The present paper begins the general study of what we call Type II sums which utilize a circle method framework and a convolution of shifted convolution sums to obtain all of the lower order terms in the asy...

Averages of Shifted Convolutions of d3(n)

We investigate the first and second moments of shifted convolutions of the generalized divisor function d3(n).

A Geometric Variant of Titchmarsh Divisor Problem

We formulate a geometric analogue of the Titchmarsh Divisor Problem in the context of abelian varieties. For any abelian variety A defined over Q, we study the asymptotic distribution of the primes of Z which split completely in the division fields of A. For all abelian varieties which contain an elliptic curve we establish an asymptotic formula for such primes under the assumption of GRH. We e...