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Kummer Theory for Number Fields and the Reductions of Algebraic Numbers II Cover

Kummer Theory for Number Fields and the Reductions of Algebraic Numbers II

By: Antonella Perucca and  Pietro Sgobba  
Open Access
|Jul 2020

References

  1. [1] CHINEN, K.—MURATA, L.: On a Distribution Property of the Residual Order of a (mod p) IV. In: Papers from the 3rd China-Japan Seminar on Number Teory, Xi’an, China, February 12–16, 2004. (Zhang, Wenpeng, et al. eds), Number Theory. Tradition and Modernization. Developments in Math. Vol. 15, Springer, New York, NY, 2006.
  2. [2] DEBRY, C.—PERUCCA, A.: Reductions of algebraic integers,J.NumberTheory 167 (2016), 259–283.10.1016/j.jnt.2016.03.001
  3. [3] MOREE, P.: Artin’s primitive root conjecture–a survey, Integers 12 (2012), no. 6, 1305–1416.10.1515/integers-2012-0043
  4. [4] MOREE, P.: On the distribution of the order and index of g (mod p) over residue classes III, J. Number Theory 120 (2006), no. 1, 132–160.10.1016/j.jnt.2005.11.005
  5. [5] PERUCCA, A.: Multiplicative order and Frobenius symbol for the reductions of number fields, (J. S. Balakrishnan et al. eds.) In: Research Directions in Number Theory, Association for Women in Mathematics, Ser. 19 (2019), pp. 161–171.10.1007/978-3-030-19478-9_8
  6. [6] PERUCCA, A.: Prescribing valuations of the order of a point in the reductions of abelian varieties and tori. J. Number Theory 129 (2009), no. 2, 469–476.10.1016/j.jnt.2008.07.004
  7. [7] PERUCCA, A.: Reductions of algebraic integers II. (I. I. Bouw et al. eds.) In: Women in Numbers Europe II, Association for Women in Mathematics, Ser. 11 (2018), pp. 10–33.10.1007/978-3-319-74998-3_2
  8. [8] PERUCCA, A.—SGOBBA, P.: Kummer theory for number fields and the reductions of algebraic numbers, Int. J. Number Theory, 15 (2019), no. 8, 1617–1633.10.1142/S179304211950091X
  9. [9] SageMath-the Sage Mathematics Software System (Version 8.9). The Sage Developers, 2019, https://www.sagemath.org.
  10. [10] ZIEGLER, V.: On the distribution of the order of number field elements modulo prime ideals, Unif. Distrib. Theory 1 (2006), no. 1, 65–85.
DOI: https://doi.org/10.2478/udt-2020-0004 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X
Language: English
Page range: 75 - 92
Submitted on: Jul 7, 2019
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Accepted on: Mar 23, 2020
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Published on: Jul 24, 2020
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2020 Antonella Perucca, Pietro Sgobba, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.