In this paper, the general Cochrane sum is defined. The main purpose is to study the mean square value problem of general Cochrane sum by using the estimates for trigonometric sums and the properties of general Kloosterman sum, and finally give a sharp asymptotic formula.
"On the mean value of general Cochrane sum." Proc. Japan Acad. Ser. A Math. Sci. 86 (1) 1 - 5, January 2010. https://doi.org/10.3792/pjaa.86.1