Manchester Number Theory Seminar - Kyle Pratt
Dates: | 25 October 2022 |
Times: | 15:00 - 16:00 |
What is it: | Seminar |
Organiser: | Department of Mathematics |
Who is it for: | University staff, External researchers, Current University students |
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Speaker: Kyle Pratt (University of Oxford)
Title: The irrationality of a divisor function series of Erdos and Kac
Abstract: For each positive integer k Erdos and Kac defined a number, call it alpha_k, which is given by an infinite sum involving the sum-of-kth-powers-of-divisors function. They conjectured alpha_k is irrational for every k. This is known conditionally under strong assumptions like the Hardy-Littlewood prime k-tuples conjecture, and was previously known unconditionally for k <= 3. We discuss our recent proof that alpha_4 is irrational. The proof relies on sieve theory and exponential sum estimates
Room: Frank Adams 2
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Frank Adams 2
Alan Turing Building
Manchester