The Behavior of Euler–Kronecker Constants of Quadratic Fields

Abstract

This thesis is a review of the work by Professor Lamzouri on the distribution of Euler–Kronecker con- stants associated with quadratic fields [5]. To study the behavior of the Euler–Kronecker constant gamma_Q(sqrtD), we construct a probabilistic random model gamma_rand(X) that reflects its key characteristics. We analyze the large moments of gamma_Q(sqrt D) and compute the Laplace transforms of both gamma_Q( sqrtD) and gamma_rand(X). Through these tools, we examine the distribution of the random model and, in turn, gain insights into the distribution of the actual constants over quadratic fields.