A congruence sum and rational approximations

Abstract

We give a reciprocity formula for a two-variable sum where the variables satisfy a linear congruence condition. We also prove that such sum is a measure of how well a rational is approximable from below and show that the reciprocity formula is a simple consequence of this fact.

7 pages, 2 figures, to appear in Rend. Circ. Mat. Palermo, II. Ser

References in corpus (2)

• On the reciprocity law for the twisted second moment of Dirichlet $L$-functions
• The mean-square of Dirichlet L-functions