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# An explicit upper bound on the least primitive root

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# The Weyl law for algebraic tori

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A basic but difficult question in the analytic theory of automorphic forms is: given a reductive group G and a representation r of its L-group, how many automorphic representations of bounded analytic conductor are there? In this talk I will present an answer to this question in the case that G is a torus over a number field.

# Factorization of Hasse-Weil zeta functions of Dwork surfaces

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As a classical example of K3 surfaces, the Dwork surface family is of interest in algebraic geometry and number theory. A lot of work has been done to understand the Hasse-Weil zeta functions of these surfaces. Recent works show that people can totally determine the algebraic part of the zeta function for a general Dwork surface. In this talk, we discuss how to use geometric method to find the explicit factorization of the algebraic part.