|DATE||August 19 (Mon), 2019|
|INSTITUTE||University of Sarajevo|
|TITLE||Kronecker's Limit Formula I|
|ABSTRACT|| Since Kronecker’s paper from 1863, the Kronecker’s first limit formula has been studied by many mathematicians and in many different contexts. A basic idea behind the formula is rather simple: loosely speaking, the constant term of the Laurent series expansion at the pole s = 1 of (some) non-holomorphic Eisenstein-type series is a function carrying an important information about the arithmetic/geometric/spectral properties of the underlying space (at which the Eisenstein-type series is defined).
In this lecture, we will describe the Kronecker limit formula for three different non-holomorphic Eisenstein-type series and derive various interesting consequences stemming from the analysis of the constant terms in the formula (they will be referred to as the Kronecker limit functions).