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site of the metric2011 program of Centre Emile Borel

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metric2011 | site of the metric2011 program of Centre Emile Borel metric2011 site of the metric2011 program of Centre Emile Borel Skip to content Home About ← Older posts Notes of Will Sawin first Hadamard lecture, 15-05-2023 Posted on May 22, 2023 by metric2011 Number theory over function fields 1. The classical theory Let us start with classical stuff. Theorem 1 (Dirichlet) a positive integer, an integer. There exist infinitely many prime numbers such that if and only if . A more precise statement is the prime number theorem on arithmetic progressions: for some explicit . In other words, remainders mod of primes are evenly distributed. The proofs of both theorems rely on properties of Dirichlet characters. Definition 2 A function is a Dirichlet character mod if for all , for all , . From a Dirichlet character, one constructs a Dirichlet -function 1.1. Properties If , the trivial character, then ...

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