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CMS Doctoral Prize Lecture / Prix de doctorat

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NATHAN NG, University of Georgia, Department of Mathematics, University of Georgia, Boyd GSRC, Athens, Georgia, USA, 30602
Limiting distributions and zeros of Artin L-functions

I will discuss how limiting distributions (probability measures) may be constructed in order to study number theoretic problems. These distributions are formed from the zeros of a class of meromorphic functions known as Artin L-functions. In fact, properties of the limiting distributions reveal properties of prime numbers. Applications to the summatory function of the Mobius function and prime counting functions attached to number field extensions will be presented.