On the F.Smarandache LCM function and its mean value

The main purpose of this paper is to use the elementary methods to study the mean value of the F.Smarandache LCM function SL(n), and give a sharper asymptotic formula for it

Diophantine equations defined by binary quadratic forms over rational function fields

We study the ``imaginary" binary quadratic form equations ax^2+bxy+cy^2+g=0 over k[t] in rational function fields, showing that a condition with respect to the Artin reciprocity map, is the only obstruction to the local-global principle for integral solutions of the equation.Comment: 14 pages, git commit 20170117/57d58b6, to appear in Acta Arithmetic