Ax-Kochen theorem

proper noun

A theorem stating that for each positive integer d there is a finite set Y_d of prime numbers, such that if p is any prime not in Y_d then every homogeneous polynomial of degree d over the p-adic numbers in at least d²+1 variables has a nontrivial zero.

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Meanings

proper nounthe Ax-Kochen theorem
  1. mathematicsA theorem stating that for each positive integer d there is a finite set Y_d of prime numbers, such that if p is any prime not in Y_d then every homogeneous polynomial of degree d over the p-adic numbers in at least d²+1 variables has a nontrivial zero.

Origin

Named after James Ax and Simon B. Kochen.

Full word history & related roots →
Cite this entry
APA

Ax-Kochen theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/Ax-Kochen%20theorem

MLA

“Ax-Kochen theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Ax-Kochen%20theorem. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “Ax-Kochen theorem,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/Ax-Kochen%20theorem.

Source: Ax-Kochen theorem on Wiktionary, CC BY-SA 4.0.