The pp-adic Riemann Hypothesis for exponential sums

Let nn and dd be the parameters defining the generic Newton polygon GNP(n,d;p){\rm GNP}(n,d;p) and the Frobenius polygon FP(n,d;p){\rm FP}(n,d;p), and let pp be a prime. The pp-adic Riemann Hypothesis. If pp is sufficiently large, then

GNP(n,d;p)=FP(n,d;p).{\rm GNP}(n,d;p)={\rm FP}(n,d;p).

The paper presents this as a conjecture following Wan's asymptotic conjecture; the supplied context records partial results, including the case n=1n=1 for sufficiently large pp and a special two-variable case, but does not indicate a resolution in general.

Sources & referencesView supporting material

Primary source

Chunlei Liu and Chuanze Niu, “The p-adic Riemann Hypothesis For Expnonential Sums”, arXiv:1912.04503 (2020).

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