Extensions of Wilson's lemma and the Ax-Katz theorem

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dc.creatorSun, Zhi-Wei
dc.date2006-08-23
dc.date.accessioned2026-07-07T07:22:02Z
dc.date.available2026-07-07T07:22:02Z
dc.descriptionA classical result of A. Fleck states that if p is a prime, and n>0 and r are integers, then $$\sum_{k=r(mod p)}\binom {n}{k}(-1)^k=0 (mod p^{[(n-1)/(p-1)]}).$$ Recently R. M. Wilson used Fleck's congruence and Weisman's extension to present a useful lemma on polynomials modulo prime powers, and applied this lemma to reprove the Ax-Katz theorem on solutions of congruences modulo p and deduce various results on codewords in p-ary linear codes with weights. In light of the recent generalizations of Fleck's congruence given by D. Wan, and D. M. Davis and Z. W. Sun, we obtain new extensions of Wilson's lemma and the Ax-Katz theorem.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/math/0608560
dc.identifierhttp://arxiv.org/abs/math/0608560
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115520
dc.subjectNumber Theory
dc.subjectCombinatorics
dc.subject11T06; 05A10; 11A07; 11S05; 41A10
dc.titleExtensions of Wilson's lemma and the Ax-Katz theorem
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