Equidistribution from the Chinese Remainder Theorem
Kannan Soundararajan (Stanford University)
Abstract: Suppose for each prime $p$ we are given a set $A_p$ (possibly empty) of residue classes mod $p$. Use these and the Chinese Remainder Theorem to form a set $A_q$ of residue classes mod $q$, for any integer $q$. Under very mild hypotheses, we show that for a typical integer $q$, the residue classes in $A_q$ will become equidistributed. The prototypical example (which this generalizes) is Hooley's theorem that the roots of a polynomial congruence mod $n$ are equidistributed on average over $n$. I will also discuss generalizations of such results to higher dimensions, and when restricted to integers with a given number of prime factors. (Joint work with Emmanuel Kowalski.)
number theory
Audience: researchers in the topic
Columbia CUNY NYU number theory seminar
Organizers: | Dorian Goldfeld*, Eric Urban, Fedor Bogomolov, Yuri Tschinkel, Alexander Gamburd, Victor Kolyvagin, Gautam Chinta |
*contact for this listing |