Asymptotic Formulas for the Fourth Power Moment of Twisted Kloosterman Sums and Related p-adic Hypergeometric Functions

The fourth power moment of twisted Kloosterman sums can be expressed as weighted sums of Hurwitz class numbers, and asymptotic formulas for these weighted sums are derived using the theory of harmonic Maass forms and mock modular forms. As a consequence, asymptotic averages of certain families of p-adic hypergeometric functions are obtained.