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2017 The probability that the number of points on a complete intersection is squarefree
Eric Schmidt
Rocky Mountain J. Math. 47(8): 2777-2796 (2017). DOI: 10.1216/RMJ-2017-47-8-2777

Abstract

We consider the asymptotic probability that integers chosen according to a binomial distribution will have certain properties: (i) that such an integer is not divisible by the $k$th power of a prime, (ii) that any $k$ of $s$ chosen integers are relatively prime and (iii) that a chosen integer is prime. We also prove an analog of the Dirichlet divisor problem for the binomial distribution. We show how these results yield corresponding facts concerning the number of points on a smooth complete intersection over a finite field.

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Eric Schmidt. "The probability that the number of points on a complete intersection is squarefree." Rocky Mountain J. Math. 47 (8) 2777 - 2796, 2017. https://doi.org/10.1216/RMJ-2017-47-8-2777

Information

Published: 2017
First available in Project Euclid: 3 February 2018

zbMATH: 06841000
MathSciNet: MR3760318
Digital Object Identifier: 10.1216/RMJ-2017-47-8-2777

Subjects:
Primary: 11N37
Secondary: 11G25

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 8 • 2017
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