Angles of Gaussian Primes
Oberseminar Zahlentheorie und Arithmetische Geometrie, 23.11.2017
Fermat showed that every prime p=1 mod 4 is a sum of two squares: p=a2+b2, and hence such a prime gives rise to an angle whose tangent is the ratio b/a. Hecke proved that these Gaussian primes are equidistributed across sectors of the complex plane, by making use of (infinite) Hecke characters and their associated L-functions.
In this talk I will present a conjecture, motivated by a random matrix model, for the variance of Gaussian primes across sectors, and discuss ongoing work about a more refined conjecture that picks up lower-order-terms. I will also introduce a function field model for this problem, and describe the analogue to Hecke's equidistribution theorem, in this setting. By applying a recent result of N. Katz concerning the equidistribution of "super even" characters (the function field analogues to Hecke characters), I will provide a result for the variance of function field Gaussian primes across sectors; a computation whose analogue in number fields is unknown beyond a trivial regime
Ezra Waxman (Tel Aviv University)
Institut für Algebra, Zahlentheorie und Diskrete Mathematik
12:00 o'clock - 13:00 o'clock
Institut für Algebra, Zahlentheorie und Diskrete Mathematik (IAZD)