6 papers
The Furstenberg-Sárközy theorem for sums of an even number of odd powers
Alexandros Kalogirou, Andrew Lott, Ákos Magyar +1
We obtain a Furstenberg-Sárközy-type result for sets whose difference set does not contain the sum of -many -th powers of positive integers, with o…
The distribution of intermediate prime factors
Nathan McNew, Paul Pollack, Akash Singha Roy
Let denote the middle prime factor of (taking into account multiplicity). More generally, one can consider, for any , the -positio…
On Benford's Law for multiplicative functions
Vorrapan Chandee, Xiannan Li, Paul Pollack +1
We provide a criterion to determine whether a real multiplicative function is a strong Benford sequence. The criterion implies that the -divisor functions, where ,…
Powerfree sums of proper divisors
Paul Pollack, Akash Singha Roy
Let denote the sum of the proper divisors of . It is natural to conjecture that for each integer , the equivalence \[ \text{ is th p…
Distribution mod of Euler's totient and the sum of proper divisors
Noah Lebowitz-Lockard, Paul Pollack, Akash Singha Roy
We consider the distribution in residue classes modulo primes of Euler's totient function and the sum-of-proper-divisors function . We prove that the value…
Joint distribution in residue classes of polynomial-like multiplicative functions
Paul Pollack, Akash Singha Roy
Under fairly general conditions, we show that families of integer-valued polynomial-like multiplicative functions are uniformly distributed in coprime residue classes mod , wher…