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We describe a simple procedure to find Aurifeuillian factors of values of cyclotomic polynomials $Φ_{d} (a)$ for integers $a$ and $d > 0$ . Assuming a suitable Riemann Hypothesis, the algorithm runs in deterministic time $\tilde{O} (d^{2} L)$ , using $O (d L)$ space, where $L ≔ log (|a| + 1)$ .

p-Ranks of Class Groups in Zdp-Extensions.

Paul Monsky (1983)

Mathematische Annalen

Predictive criteria for the representation of primes by binary quadratic forms

Joseph B. Muskat, Blair K. Spearman, Kenneth S. Williams (1995)

Acta Arithmetica

Preface

J. Berstel, T. Harju, J. Karhumäki (2008)

RAIRO - Theoretical Informatics and Applications

Prehomogeneous spaces associated with nilpotent orbits in simple real Lie algebras $E_{6 (6)}$ and $E_{6 (- 26)}$ and their relative invariants.

Jackson, Steven Glenn, Noël, Alfred G. (2006)

Experimental Mathematics

Prehomogeneous vector spaces and field extensions.

David J. Wright, Akihiko Yukie (1992)

Inventiones mathematicae

Première partie du chapitre XIII de la Note sur la théorie des résidus quadratiques.

Angelo Genocchi (1889)

Journal für die reine und angewandte Mathematik

Preservation of log-concavity on summation

Oliver Johnson, Christina Goldschmidt (2006)

ESAIM: Probability and Statistics

We extend Hoggar's theorem that the sum of two independent discrete-valued log-concave random variables is itself log-concave. We introduce conditions under which the result still holds for dependent variables. We argue that these conditions are natural by giving some applications. Firstly, we use our main theorem to give simple proofs of the log-concavity of the Stirling numbers of the second kind and of the Eulerian numbers. Secondly, we prove results concerning the log-concavity of the sum of...

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