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math.NT2026
On partial T-adic exponential sums and partial exponential sums with p-power conductor
C. Douglas Haessig
Liu and Wan introduced T-adic exponential sums as a way to interpolate all character sums with character having p-power conductor. In this paper, we generalize their T-adic theory…
math.NT2026
-adic Theory for Partial Toric Exponential Sums
C. Douglas Haessig
Wan proved the rationality of partial toric -functions using -adic techniques. In this paper, we present a -adic proof in the spirit of Dwork. We demonstrate that parti…