On the distribution of Salem numbers

Götze F, Gusakova A (2020)
Journal of Number Theory 216: 192-215.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Götze, FriedrichUniBi; Gusakova, Anna
Abstract / Bemerkung
In- this paper we study the problem of counting Salem numbers of fixed degree. Given a set of disjoint intervals I-1, ..., I-k subset of [0; pi], 1 <= k <= m let Sal(m, k)(Q, I-1, ..., I-k) denote the set of ordered (k + 1)-tuples (alpha(0), ..., alpha(k)) of conjugate algebraic integers, such that alpha(0 )is a Salem number of degree 2m + 2 satisfying alpha(0) <= Q for some positive real number Q and arg alpha(i) is an element of I-i We derive the following asymptotic approximation #Sal(m,k) (Q, I-1, ..., I-k) =omega(m) Q(m+1) integral(I1 )... integral(Ik )rho(m,k)(theta)d theta +O(Q(m)), Q ->infinity, providing explicit expressions for the constant omega(m) and the function rho(m,k) (theta). Moreover we derive a similar asymptotic formula for the set of all Salem numbers of fixed degree and absolute value bounded by Q as Q ->infinity. (C) 2020 Elsevier Inc. All rights reserved.
Stichworte
Salem number; Counting formula; Correlation function; Jacobi random; matrix ensemble; Weil height
Erscheinungsjahr
2020
Zeitschriftentitel
Journal of Number Theory
Band
216
Seite(n)
192-215
ISSN
0022-314X
eISSN
1096-1658
Page URI
https://pub.uni-bielefeld.de/record/2945598

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Götze F, Gusakova A. On the distribution of Salem numbers. Journal of Number Theory. 2020;216:192-215.
Götze, F., & Gusakova, A. (2020). On the distribution of Salem numbers. Journal of Number Theory, 216, 192-215. doi:10.1016/j.jnt.2020.02.012
Götze, F., and Gusakova, A. (2020). On the distribution of Salem numbers. Journal of Number Theory 216, 192-215.
Götze, F., & Gusakova, A., 2020. On the distribution of Salem numbers. Journal of Number Theory, 216, p 192-215.
F. Götze and A. Gusakova, “On the distribution of Salem numbers”, Journal of Number Theory, vol. 216, 2020, pp. 192-215.
Götze, F., Gusakova, A.: On the distribution of Salem numbers. Journal of Number Theory. 216, 192-215 (2020).
Götze, Friedrich, and Gusakova, Anna. “On the distribution of Salem numbers”. Journal of Number Theory 216 (2020): 192-215.

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