Peter Koymans

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Peter Koymans, Université
de Leiden, PAYS-BAS

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The spin of prime ideals and applications

Let **K** be a cyclic, totally real extension of **Q** of degree at least
3, and let σ be a generator of Gal(**K**/**Q**).

We further assume that the totally positive units are exactly the squares of
units. In this case, Friedlander,

Iwaniec, Mazur and Rubin define the spin of an odd principal ideal
*a* to be
spin(σ, *a*) = (α/σ(*a*))_{K}, where

α is a totally positive generator of *a* and (*/*) is the
quadratic residue symbol in **K**. Friedlander, Iwaniec,

Mazur and Rubin prove equidistribution of spin(σ, *p*) as *p*
varies over the odd principal prime ideals of **K**.

In this talk I will show how to extend their work to more general
fields. I will then give various arithmetic

applications.

This is a joint work with Djordjo Milovic.