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Counting shifted-prime divisors

Posted in
Kai (Steve) Fan
Dartmouth College/MPIM
Wed, 07/02/2024 - 14:30 - 15:30
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

A shifted prime is a number of the form p-1, where p is prime. For every positive integer n, let omega*(n) denote the number of positive divisors of n that are shifted primes. First studied by Prachar in an influential paper from 70 years ago, the function omega* shares some interesting features with the divisor function tau and the prime-divisor function omega, but its distribution still remains a mystery. The study of this function was recently picked up by Murty and Murty who proved lower and upper bounds for the second moment of omega*, and shortly after their work, Ding obtained a refinement of their lower bound and suggested a possible asymptotic formula. In this talk, we continue this trend of study by investigating the higher moments of omega* and other related problems. This is joint work with Carl Pomerance.

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