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 Electronic Communications in Probability > Vol. 11 (2006) > Paper 29 open journal systems 


The expected number of zeros of a random system of p-adic polynomials

Steven N. Evans, University of California at Berkeley


Abstract
We study the simultaneous zeros of a random family of d polynomials in d variables over the p-adic numbers.For a family of natural models, we obtain an explicit constant for the expected number of zeros that lie in the d-fold Cartesian product of the p-adic integers. Considering models in which the maximum degree that each variable appears is N, this expected value is
pd ⌊ logp N ⌋ (1 + p-1 + p-2 + ... + p-d)-1
for the simplest such model.


Full text: PDF

Pages: 278-290

Published on: November 30, 2006
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Electronic Communications in Probability. ISSN: 1083-589X