This event is from the archives of The Notice Board. The event has already taken place and the information contained in this post may no longer be relevant or accurate.
Lethbridge Number Theory and Combinatorics Seminar
Date:
April 9, 2018
Time:
12:00-12:50pm
Lecturer(s):
Jean-Marc Deshouillers (University of Bordeaux)
Location:
University of Lethbridge
Topic:
Values of arithmetic functions at consecutive arguments
Description:
We shall place in a general context the following result recently obtained jointly with Yuri Bilu (Bordeaux), Sanoli Gun (Chennai) and Florian Luca (Johannesburg).
Theorem. Let tau be the classical Ramanujan tau-function and let k be a positive integer such that tau(n) is nonzero for all n less than or equal to k/2.
(This is known to be true for k < 10^23, and, conjecturally, for all k.) Further, let s be a permutation of the set {1,...,k}. We show that there exist infinitely many positive integers m such that
|\tau(m+s(1))| < |\tau(m+s(2))| < ... < |\tau(m+s(k))|.
The proof uses sieve method, Sato-Tate conjecture, recurrence relations for the values of tau at prime power values.
Other Information:
Location: B543 University Hall
Web page: http://www.cs.uleth.ca/~nathanng/ntcoseminar/
Contact:
Barb Hodgson | hodgsonb@uleth.ca | (403) 329-2470 | uleth.ca/artsci/math-computer-science
