Tomos Parry

collaborators

4 papers

math.NT2024

Primes in arithmetic progressions on average II

Tomos Parry

A deep conjecture of Montgomery and Soundararajan on the distribution of prime numbers in short intervals of length $h$ says that the third moment is bounded by $\ll h^{\frac {3}{2…

math.NT2024

A note on the distribution of $d_{3} (n)$ in arithmetic progressions

Tomos Parry

Nguyen has shown that on averaging over $a = 1, ..., q$ the 3-fold divisor function has exponent of distribution 2/3, following \cite {banks}. We follow [2] which leads to stronger bou…

math.NT2024

Primes in arithmetic progressions on average I

Tomos Parry

Let $E_{x} (q, a)$ be the error term when counting primes in arithmetic progressions and let $M (Q) = \sum_{q \leq Q} ϕ (q) \sum_{a = 1}^{q} E_{x} (q, a)^{3}$ . We show that $M (Q) << Q^{3} (x / Q)^{7/5}$ for la…

math.NT2024

The distribution of $d_{4} (n)$ in arithmetic progressions

Tomos Parry

We use the Petrow-Young [10] subconvexity bound for Dirichlet $L$ -functions to show that $d_{4} (n)$ has exponent of distribution $4/7$ when we allow an average over $a$ mod $q$ , ther…

Primes in arithmetic progressions on average II

A note on the distribution of d3​(n) in arithmetic progressions

Primes in arithmetic progressions on average I

The distribution of d4​(n) in arithmetic progressions

A note on the distribution of $d_{3} (n)$ in arithmetic progressions

The distribution of $d_{4} (n)$ in arithmetic progressions