# Meeting Details

Title: Binary Egyptian Fractions Algebra and Number Theory Seminar Jingjing Huang, Penn State University In this talk, we will survey various results about the diophantine equation a/n=1/x+1/y with a fixed and n varying, and in particular its number of solutions R(n;a). One can show that the behavior of R(n;a) resembles that of the divisor function $d(n)$ in many aspects. More precisely, we will investigate the first moment estimate of R(n;a) and also higher moments. Then, we can show that log R(n;a) has a Gaussian distribution analoguously to the classical theorem of Erdos and Turan. And last, one can study the exceptional set E_a(N), namely the number of n up to N such that R(n;a)=0. We will improve a result by Hofmeister and Stoll, in which it is shown that the E_a(N)<