L-functions in Analytic Number Theory Seminar: Nicol Leong

Bounds on the logarithmic derivative and the reciprocal of the Riemann zeta function are studied as they have a wide range of applications, such as computing bounds for Mertens function. In this talk, we are mainly concerned with explicit bounds. Obtaining decent bounds are tricky, as they are only valid in a zero-free region, and the constants involved tend to blow up as one approaches the edge of the region, and a potential zero. We will discuss such bounds, their uses, and the computational and analytic techniques involved. Finally, we also show how to obtain a power savings in the case of the reciprocal of zeta.