Kyle Pratt

activity

20182026

most citedWeighted central limit theorems for central values of

L

-functions

1 citations · 1 across the 12 of their papers we have counts for

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3 papers · 1 filter

math.NT2022

A problem of Erdős-Graham-Granville-Selfridge on integral points on hyperelliptic curves

Hung M. Bui, Kyle Pratt, Alexandru Zaharescu

Erdős, Graham, and Selfridge considered, for each positive integer $n$ , the least value of $t_{n}$ so that the integers $n + 1, n + 2, \dots, n + t_{n}$ contain a subset the product of whos…

math.NT2022

The irrationality of a divisor function series of Erdős and Kac

Kyle Pratt

For positive integers $k$ and $n$ let $σ_{k} (n)$ denote the sum of the $k$ th powers of the divisors of $n$ . Erdős and Kac asked whether, for every $k$ , the number $α_k = \sum_{n\geq…

math.NT2022

Power savings for counting solutions to polynomial-factorial equations

Hung M. Bui, Kyle Pratt, Alexandru Zaharescu

Let $P$ be a polynomial with integer coefficients and degree at least two. We prove an upper bound on the number of integer solutions $n \leq N$ to $n! = P (x)$ which yields a power…