# Jacobi-Kubota symbols

Posted in
Speaker:
Djordjo Milovic
Affiliation:
University College London
Date:
Tue, 2018-09-04 12:05 - 12:35
Location:
MPIM Lecture Hall

In their work on the primes of the form $X^2+Y^4$, Friedlander and Iwaniec associated to each odd primary element $r+si$ of the Gaussian integers the Jacobi symbol $$\left(\frac{s}{|r|}\right),$$ and named it the Jacobi-Kubota symbol. They proceeded to prove, via a variant of Vinogradov's method, that this symbol is equidistributed (in the set $\{-1, 1\}$) as $r+si$ varies among primes in the Gaussian integers. We will consider a generalization of this symbol to arbitrary quadratic rings, and prove a similar equidistribution result. We will also discuss the applications of this result to arithmetic statistics.

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