The Riemann Hypothesis, Ramanujan conjecture and applications

Wen-Ching Winnie Li

Department of Mathematics

Pennsylvania State University

wli@math.psu.edu

The Riemann Hypothesis and Ramanujan conjecture are two celebrated open problems in number theory which have important and farreaching consequences. They also appear in different settings. In this talk we discuss their relations and show some applications derived from the occasions where the conjectures hold. This is a survey talk highlighting the interplay between number theory and combinatorics.