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See detailOn the distribution of the order and index for the reductions of algebraic numbers
Sgobba, Pietro UL

in Journal of Number Theory (2021)

Let \alpha_1,...,\alpha_r be algebraic numbers in a number field K generating a subgroup of rank r in K*. We investigate under GRH the number of primes p of K such that each of the orders of (\alpha_i mod ... [more ▼]

Let \alpha_1,...,\alpha_r be algebraic numbers in a number field K generating a subgroup of rank r in K*. We investigate under GRH the number of primes p of K such that each of the orders of (\alpha_i mod p) lies in a given arithmetic progression associated to (\alpha_i). We also study the primes p for which the index of (\alpha_i mod p) is a fixed integer or lies in a given set of integers for each i. An additional condition on the Frobenius conjugacy class of p may be considered. Such results are generalizations of a theorem of Ziegler from 2006, which concerns the case r=1 of this problem. [less ▲]

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See detailAddendum to: Reductions of algebraic integers
Perucca, Antonella UL; Sgobba, Pietro UL; Tronto, Sebastiano UL

in Journal of Number Theory (2020)

Let K be a number field, and let G be a finitely generated and torsion-free subgroup of K*. We consider Kummer extensions of G of the form K(\zeta_{2^m}, \sqrt[2^n]G)/K(\zeta_{2^m}), where n \leq m. In ... [more ▼]

Let K be a number field, and let G be a finitely generated and torsion-free subgroup of K*. We consider Kummer extensions of G of the form K(\zeta_{2^m}, \sqrt[2^n]G)/K(\zeta_{2^m}), where n \leq m. In the paper "Reductions of algebraic integers" (J. Number Theory, 2016) by Debry and Perucca, the degrees of those extensions have been evaluated in terms of divisibility parameters over K(\zeta_4). We prove how properties of G over K explicitly determine the divisibility parameters over K(\zeta_4). This result has a clear computational advantage, since no field extension is required. [less ▲]

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See detailReductions of algebraic integers
Debry, Christophe; Perucca, Antonella UL

in Journal of Number Theory (2016)

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See detailThe order of the reductions of an algebraic integer
Perucca, Antonella UL

in Journal of Number Theory (2015)

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See detailTame Galois realizations of $ GL_2(\Bbb F_l)$ over $\Bbb Q$
Arias De Reyna Dominguez, Sara UL; Vila, Núria

in Journal of Number Theory (2009), 129(5), 1056--1065

This paper concerns the tame inverse Galois problem. For each prime number l, we construct infinitely many semistable elliptic curves over Q with good supersingular reduction at l. The Galois action on ... [more ▼]

This paper concerns the tame inverse Galois problem. For each prime number l, we construct infinitely many semistable elliptic curves over Q with good supersingular reduction at l. The Galois action on the l-torsion points of these elliptic curves provides tame Galois realizations of GL_2(F_l) over Q. [less ▲]

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See detailAppendice : quelques données statistiques
Fermigier, Stéphane; Leprévost, Franck UL; FIEKER, Claus

in Journal of Number Theory (1999), 78

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See detailRevêtements de courbes elliptiques à multiplication complexe par des courbes hyperelliptiques et sommes de caractères
Leprévost, Franck UL; Morain, François

in Journal of Number Theory (1997), 64(2), 165-182

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