[Turkmath:485] İYTE Matematik Bolumu-Seminer Duyurusu

[Engin BUYUKASIK]

You are cordially invited to the seminar by Dr. Emek 
Demirci Akarsu, from University of Bristol.

Date/Time: 8 May 2015 (Friday) / 14.30,
Place: Math. Dept. Seminar Room 122

TITLE: Rationals on horocycles and incomplete Gauss sums.


ABSTRACT: In this seminar I will talk about the connection 
between the limiting distributions of rational points on 
horocycle flows and the value distribution of incomplete 
Gauss sums. A key property of the horocycle fow on a 
finite-area hyperbolic surface is that long closed 
horocycles are uniformly distributed. We embed rational 
points on such horocycles on the modular surface and 
investigate their equidistribution properties.

On the other hand, it is well known that the classical 
Gauss sums can be evaluated in closed form depending on 
the residue class of the number of terms in the sum modulo 
4. This is not the case for the incomplete Gauss sums, 
where we restrict the range of summation to a sub-interval 
and study their limiting behavior at random argument as 
the number of terms goes to infinity.

If the time permits, I also establish an analogue of the 
weak invariance principle for incomplete Gauss sums.