Shifted convolution and the Titchmarsh divisor problem over F_q[t]

Abstract

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

22 pages, updated version

References in corpus (1)

• The autocorrelation of the Möbius function and Chowla's conjecture for the rational function field in characteristic 2

Cited by in corpus (17)

• Sums of divisor functions in $F_q[t]$ and matrix integrals
• Arithmetic functions in short intervals and the symmetric group
• Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges
• The autocorrelation of the Möbius function and Chowla's conjecture for the rational function field in characteristic 2
• On the Bateman-Horn conjecture for polynomials over large finite fields
• Combinatorial identities and Titchmarsh's divisor problem for multiplicative functions
• A trace formula for the distribution of rational $G$-orbits in ramified covers, adapted to representation stability
• Chebotarev density theorem in short intervals for extensions of ${\mathbb{F}}_q(T)$
• Correlation of arithmetic functions over ${\mathbb{F}}_q[T]$
• Probabilities of incidence between lines and a plane curve over finite fields
• Cubic twin prime polynomials are counted by a modular form
• Uniform estimates for almost primes over finite fields
• Prime and Möbius correlations for very short intervals in ${\mathbb{F}}_q[x]$
• Note on the Theory of Correlation Functions
• Arithmetic correlations over large finite fields
• On locally repeated values of arithmetic functions over ${\mathbb{F}}_q[T]$
• Polynomial values modulo primes on average and sharpness of the larger sieve