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Graduate Student Number Theory Seminar

L-functions, the explicit formula, and the highest-lowest zero

George Hauser - Rutgers University

Location:  Hill 425
Date & time: Thursday, 18 October 2018 at 11:00AM - 11:50AM

Abstract: The celebrated explicit formula for the Riemann zeta function relates sums over prime powers to sums over zeta’s zeros. A similar explicit formula exists for general L-functions. In this expository talk I will explain the explicit formula, and show how it applies to the problem of the “highest-lowest zero” of L-functions: how large can the imaginary part be of the first critical zero of an L-function? The answer to this question is most likely that the Riemann zeta function has the highest-lowest zero, and while this is proved in many cases, it is not known in full generality.

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