Practical numbers and distribution of exponential sums

Tuesday, November 15, 2016 - 2:00pm
MSB 110
Zhenyu Guo (University of Missouri, Columbia)

p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Arial; -webkit-text-stroke: #000000}
span.s1 {font-kerning: none}

A positive integer n is called practical if every positive integer m smaller than or equal to n can be expressed as a sum of distinct positive divisors of n. We show that the lower bound of the number of prime numbers p such that p-a is practical. I will show some other results related to estimations of exponential sums.