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Simultaneous p-Orderings and Equidistribution

In: Algebraic, Number Theoretic, and Topological Aspects of Ring Theory

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  • Anna Szumowicz

    (Mathematics and Astronomy, Caltech, The Division of Physics)

Abstract

Let D be a Dedekind domain. Roughly speaking, a simultaneous 𝔭 $$\mathfrak {p}$$ -ordering is a sequence of elements from D which is equidistributed modulo every power of every prime ideal in D as well as possible. Bhargava in (Journal für die reine und angewandte Mathematik 490 (1997), 101–128) asked which subsets of the Dedekind domains admit simultaneous 𝔭 $$\mathfrak {p}$$ -orderings. We give an overview on the progress in this problem. We also explain how it relates to the theory of integer-valued polynomials and list some open problems.

Suggested Citation

  • Anna Szumowicz, 2023. "Simultaneous p-Orderings and Equidistribution," Springer Books, in: Jean-Luc Chabert & Marco Fontana & Sophie Frisch & Sarah Glaz & Keith Johnson (ed.), Algebraic, Number Theoretic, and Topological Aspects of Ring Theory, pages 427-442, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-28847-0_22
    DOI: 10.1007/978-3-031-28847-0_22
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