p-adic Valuation of Exponential Sums in One Variable Associated to Binomials

Francis N. Castro; Raúl Figueroa; Puhua Guan

doi:10.1515/udt-2017-0003

Abstract

In this paper we compute the p-adic valuation of exponential sums associated to binomials F(X) = aX^d₁ + bX^d₂ over F_p. In particular, its p-adic valuation is constant for a, b ∈ F∗_p . As a byproduct of our results, we obtain a lower bound for the sizes of value sets of binomials over F_q.

References

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p-adic Valuation of Exponential Sums in One Variable Associated to Binomials

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