A note on the Cochrane sum and its hybrid mean value formula

On a Sum Analogous to Dedekind Sum and Its Mean Square Value Formula

A Note on the Hypergeometric Mean Value

in terms of power means and other related means have precipitated the search for similar bounds for the more general 2F1(α, β; γ; r). In an early paper, B. C. Carlson considered the approximation of the hypergeometric mean values ( 2F1(−a, b; b + c; r)) in terms of means of order t, given by Mt(s, r) := {(1 − s) + s(1 − r)t}1/t. In this note, a refinement of one such approximation is establishe...

On the Hybrid Mean Value of Cochrane Sums and Two-term Exponential Sums

A mean value formula for elliptic curves

It is proved in this paper that for any point on an elliptic curve, the mean value of x-coordinates of its n-division points is the same as its x-coordinate.

A hybrid mean value involving a new Gauss sums and Dedekind sums

‎In this paper‎, ‎we introduce a new sum‎ ‎analogous to Gauss sum‎, ‎then we use the properties of the‎ ‎classical Gauss sums and analytic method to study the hybrid mean‎ ‎value problem involving this new sums and Dedekind sums‎, ‎and‎ ‎give an interesting identity for it.