### Hensel's classical lemma – a variant

Heilbronn Number Theory Seminar

13th March 2019, 4:00 pm – 5:00 pm

Howard House, 4th Floor Seminar Room

Related to the Igusa conjectures, Denef and Sperber conjectured a sharp bound for exponential sums mod p^m for general multivariate polynomials with integer coefficients (their local sum conjecture). A key step in verifying this conjecture in two variables is to employ a variant of the classical lemma of Hensel but where the derivative is allowed to degenerate.

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