# Manchester Number Theory Seminar - Kyle Pratt

Dates: | 25 October 2022 |
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Times: | 15:00 - 16:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Current University students |

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