Notice Board

Guest: Paul Peringuey, UNBC
Topic: On the exceptional set for sums of two totients
Date: Monday, Oct. 26, in Markin Hall M1060
Time: Noon - 1 p.m.

We prove that all but $O(X^{3/5} (\log X)^9)$ even integers up to $X$ are sums of two totients. In fact, we prove the stronger statement that all but $O(X^{3/5} (\log X)^9)$ odd integers up to $X$ are the sum of a prime and a totient. The gain over the Goldbach case comes from replacing one binary problem by a family of them, $p_1 + 2^j p_2 = n + 2^j$, of which only a bounded number can fail simultaneously. We follow Pintz's treatment of sums of three primes with a bounded third prime. This is joint work with Alia Hamieh and Stanley Yao Xiao.