About

Nancy Childress works in algebraic number theory and p-adic analysis. Number theory is one of the oldest branches of mathematics. Algebraic number theory, which employs the theory of abstract algebraic structures as a means to study properties of the integers, is more modern, as is the theory of p-adic analysis, wherein the notion of distance is redefined so that it encodes information about divisibility of integers by a given prime. Historically, number theory was viewed as a purely theoretical pursuit. Currently, it plays a central role in cryptology and digital communications. Application of p-adic analysis to quantum mechanics is a contemporary topic of research within the physics community. In addition to papers on algebraic number theory and p-adic analysis, Childress has authored a graduate text on class field theory, and has co-edited a collection of research articles in arithmetic geometry.

Research topics

• Mathematics
• Pure mathematics
• Computer science
• Arithmetic
• Combinatorics

Selected publications

• Class Field Theory

  2014-03-01 · 19 citations

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  A Brief Review.- Dirichlet#x2019 s Theorem on Primes in Arithmetic Progressions.- Ray Class Groups.- The Id#x00E8 lic Theory.- Artin Reciprocity.- The Existence Theorem, Consequences and Applications.- Local Class Field Theory.

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• On λ-invariants associated to linear extensions of the product ordering on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">N</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:math>

  Journal of Number Theory · 2014-07-03

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• Class field theory / Nancy Childress

  2009-01-01

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• Local Class Field Theory

  2008-10-10

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• Dirichlet’s Theorem on Primes in Arithmetic Progressions

  2008-10-10

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• The Existence Theorem, Consequences and Applications

  2008-10-10

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• A Brief Review

  2008-10-10

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• Artin Reciprocity

  2008-10-10

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• The Idèlic Theory

  2008-10-27

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• Ray Class Groups

  2008-10-10

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Frequent coauthors

• Jeffrey Stopple

  2 shared

• John W. Jones

  University of Warwick

  2 shared

• Scott Zinzer

  Aurora University

  1 shared

• Robert S. Gold

  1 shared

Awards & honors

• NSF (3/15/1993 - 11/30/1993)