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The distribution of values of zeta and L-functions

50 Years of Number Theory and Random Matrix Theory Conference Topic: The distribution of values of zeta and L-functions Speaker: Kannan Soundararajan Affiliation: Stanford University Date: June 21, 2022 I will survey recent progress on understanding the value distribution of zeta and L-functions. In particular I will discuss the problem of moments of the zeta function on the critical line, and central values of L-functions, where the last twenty five years have seen a conjectural understanding of the asymptotics of these moments, together with progress on obtaining good upper and lower bounds in many situations.