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TR20-092 | 16th June 2020
Ashish Dwivedi, Nitin Saxena

#### Computing Igusa's local zeta function of univariates in deterministic polynomial-time

Igusa's local zeta function $Z_{f,p}(s)$ is the generating function that counts the number of integral roots, $N_{k}(f)$, of $f(\mathbf x) \bmod p^k$, for all $k$. It is a famous result, in analytic number theory, that $Z_{f,p}$ is a rational function in $\mathbb{Q}(p^s)$. We give an elementary proof of this fact ... more >>>

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