Régis de la Bretèche: Gál’s sums and applications

Abstract: We evaluate the asymptotic size of various sums of Gál type, in particular

\(S( \mathcal{M} ):=\sum_{m,n\in \mathcal{M}} \sqrt{\frac{(m,n)}{[m,n]}},\) 

where \(\mathcal{M}\) is a finite set of integers. Elaborating on methods recently developed by Bondarenko and Seip, we obtain an asymptotic formula for
\(\log\Big(\sup_{| \mathcal{M}|= N}{S( \mathcal{M} )/N}\Big)\)
and derive new applications.

This is a joint work with Gérald Tenenbaum