[Turkmath:531] Seminar at MSGSU, Thursday, May 28, 16:00

[Mohan Ravichandran]

Dear All,

    Emek Demirci from Bristol will talk this Thursday at the Mimar Sinan
math department's weekly seminar.









*TITLE: Rational points 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 flow
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.*


Place : 106, Bomonti campus, MSGSU
Time : 16:00, Thursday, May 28

Best,
Mohan Ravichandran
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