Duke Mathematical Journal

Detecting squarefree numbers

Andrew R. Booker, Ghaith A. Hiary, and Jon P. Keating

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Abstract

We present an algorithm, based on the explicit formula for L-functions and conditional on the generalized Riemann hypothesis, for proving that a given integer is squarefree with little or no knowledge of its factorization. We analyze the algorithm both theoretically and practically and use it to prove that several RSA challenge numbers are not squarefull.

Article information

Source
Duke Math. J., Volume 164, Number 2 (2015), 235-275.

Dates
First available in Project Euclid: 30 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1422627048

Digital Object Identifier
doi:10.1215/00127094-2856619

Mathematical Reviews number (MathSciNet)
MR3306555

Zentralblatt MATH identifier
06416948

Subjects
Primary: 11Y16: Algorithms; complexity [See also 68Q25] 11M06: $\zeta (s)$ and $L(s, \chi)$
Secondary: 11Y35: Analytic computations 11M50: Relations with random matrices

Citation

Booker, Andrew R.; Hiary, Ghaith A.; Keating, Jon P. Detecting squarefree numbers. Duke Math. J. 164 (2015), no. 2, 235--275. doi:10.1215/00127094-2856619. https://projecteuclid.org/euclid.dmj/1422627048


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