Mock characters and the Kronecker symbol

Jean-Paul Allouche, Leo Goldmakher

Published 2016-08-13Version 1

We introduce and study a family of functions we call the "mock characters". These functions satisfy a number of interesting properties, and of all completely multiplicative arithmetic functions seem to come as close as possible to being Dirichlet characters. Along the way we prove a few new results concerning the behavior of the Kronecker symbol.