Tomos Parry

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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

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 $M (Q) = \sum_{q \leq Q} I ¨ (q) \sum_{a = 1}^{q} E_{x} (q, a)^{3}$ . We show that $M (Q) << Q^{3} (x / Q)^{7/5}$ for l…

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…

Primes in arithmetic progressions on average II

Primes in arithmetic progressions on average I

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

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