An asymptotic property on a reciprocity law for the Bettin--Conrey
cotangent sum
An asymptotic property on a reciprocity law for the Bettin--Conrey
cotangent sum
In 2013 Bettin and Conrey have introduced a cotangent sum $c \colon \mathbb{Q}_{>0}\to \mathbb{R}$, which can be regarded as a variant of the Dedekind sum. They have discovered that the cotangent sum satisfies a kind of reciprocity laws. Roughly speaking, the reciprocity law for $c(x)$ means that there is a …