Some arithmetic properties of numbers of the form ⌊pc⌋

Date: 
Tuesday, March 31, 2015 - 2:00pm
Location: 
MSB 110
Speaker: 
Victor Guo (University of Missouri)

<p>For fixed <em>c</em>∈(1,149/87), we derive an asymptotic formula for the number of primes <em>p</em>≤<em>x</em> such that ⌊<em>p</em><em>c</em>⌋ is squarefree, where ⌊.⌋ is the floor function. We also prove that there are infinite many <em>p</em> such that ⌊<em>p</em><em>c</em>⌋ is an almost prime.</p>