<html dir="ltr">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-9">
<style type="text/css" id="owaParaStyle"></style>
</head>
<body fpstyle="1" ocsi="0">
<div style="direction: ltr;font-family: Tahoma;color: #000000;font-size: 10pt;">
<div align="center" style="padding: 0px; margin: 0px; color: rgb(102, 102, 102); font-family: Cambria, Georgia, serif; font-size: 14px; height: 150px; background-color: rgb(255, 255, 255);">
<img src="http://www.turkmath.org/beta/images/kurumlogos/gte.jpg" alt="" style="padding: 0px; margin: 0px;"></div>
<h4 class="heading kirmiziarka" align="center" style="padding: 10px 15px; margin: -10px 0px 0px -10px; font-size: 16px; font-family: Verdana, Geneva, sans-serif; width: 970px; color: rgb(255, 255, 255); text-align: center; background-image: url(http://www.turkmath.org/beta/images/kirmiziarkaplan2.png); background-color: rgb(255, 255, 255);">
Gebze Technical University Department Seminars</h4>
<div class="baslik" style="padding: 55px 10px 10px; margin: 0px auto; width: 750px; font-size: 18pt; font-family: Cambria, Georgia, serif; font-weight: bold; line-height: 24pt; text-align: center; color: rgb(102, 102, 102); background-color: rgb(255, 255, 255);">
Incomplete Gauss sums and their relation to horocycles</div>
<div class="konusmaci" style="padding: 20px 10px 10px; margin: 0px auto; width: 850px; font-size: 16pt; font-family: Cambria, Georgia, serif; font-weight: bold; text-transform: capitalize; text-align: center; color: rgb(102, 102, 102); background-color: rgb(255, 255, 255);">
Emek Demirci Akarsu</div>
<div class="konusmacikurum" style="padding: 0px 10px 10px; margin: 0px auto; width: 550px; font-size: 12pt; font-weight: bold; text-align: center; color: rgb(102, 102, 102); font-family: Cambria, Georgia, serif; background-color: rgb(255, 255, 255);">
Recep Tayyip Erdogan University, Turkey</div>
<div class="ozet" style="padding: 25px 10px 35px; margin: 0px 115px; width: 740px; font-size: 14pt; font-family: Cambria, Georgia, serif; text-align: justify; line-height: 20pt; color: rgb(102, 102, 102); background-color: rgb(255, 255, 255);">
<span class="bold" style="padding: 0px; margin: 0px; font-weight: bold;">Özet : </span>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.</div>
<table width="759" border="0" cellspacing="5" style="padding: 0px; margin: 0px; color: rgb(102, 102, 102); font-family: Cambria, Georgia, serif; font-size: 14px; background-color: rgb(255, 255, 255);">
<tbody style="padding: 0px; margin: 0px;">
<tr style="padding: 0px; margin: 0px;">
<td width="16%" align="left" valign="top" style="padding: 0px; margin: 0px;"> </td>
<td width="7%" height="20" align="left" valign="top" class="bold" style="padding: 0px; margin: 0px; font-weight: bold;">
Tarih</td>
<td width="2%" align="left" valign="top" style="padding: 0px; margin: 0px;">:</td>
<td width="75%" height="20" align="left" valign="top" style="padding: 0px; margin: 0px;">
04.12.2015</td>
</tr>
<tr style="padding: 0px; margin: 0px;">
<td width="16%" align="left" valign="top" style="padding: 0px; margin: 0px;"> </td>
<td width="7%" height="20" align="left" valign="top" class="bold" style="padding: 0px; margin: 0px; font-weight: bold;">
Saat</td>
<td width="2%" align="left" valign="top" style="padding: 0px; margin: 0px;">:</td>
<td width="75%" height="20" align="left" valign="top" style="padding: 0px; margin: 0px;">
14:00</td>
</tr>
<tr style="padding: 0px; margin: 0px;">
<td width="16%" align="left" valign="top" style="padding: 0px; margin: 0px;"> </td>
<td width="7%" height="20" align="left" valign="top" class="bold" style="padding: 0px; margin: 0px; font-weight: bold;">
Yer</td>
<td width="2%" align="left" valign="top" style="padding: 0px; margin: 0px;">:</td>
<td width="75%" height="20" align="left" valign="top" style="padding: 0px; margin: 0px;">
Gebze Technical University, Department of Mathematics Colloquium</td>
</tr>
<tr style="padding: 0px; margin: 0px;">
<td width="16%" align="left" valign="top" style="padding: 0px; margin: 0px;"> </td>
<td width="7%" height="20" align="left" valign="top" class="bold" style="padding: 0px; margin: 0px; font-weight: bold;">
Dil</td>
<td width="2%" align="left" valign="top" style="padding: 0px; margin: 0px;">:</td>
<td width="75%" height="20" align="left" valign="top" style="padding: 0px; margin: 0px;">
Turkish</td>
</tr>
</tbody>
</table>
</div>
</body>
</html>