Reference : On the distribution of the order and index for the reductions of algebraic numbers
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/43472
On the distribution of the order and index for the reductions of algebraic numbers
English
Sgobba, Pietro mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2021
Journal of Number Theory
Elsevier
Yes (verified by ORBilu)
International
0022-314X
1096-1658
Atlanta
GE
[en] number field ; reduction ; multiplicative order ; density ; Kummer theory
[en] 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.
Researchers
http://hdl.handle.net/10993/43472

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