Asymptotic moment of fourth power twisted Kloosterman sum

Abstract: In this paper, we study the asymptotic behavior of the fourth power moment of twisted Kloosterman sums. We express this moment in terms of weighted sums involving Hurwitz class numbers. To derive the asymptotic formula, we employ the theory of harmonic Maass forms and mock modular forms. As a consequence, we also obtain asymptotic average values for certain families of hypergeometric functions over large finite fields.