Counting Extensions of $\mathfrak{p}$-Adic Fields with Given Invariants

Brian Sinclair

Counting Extensions of $\mathfrak{p}$-Adic Fields with Given Invariants

Number Theory 2015-12-23 v1

Authors: Brian Sinclair

Abstract

We give two specializations of Krasner's mass formula. The first formula yields the number of extensions of a $\mathfrak{p}$ -adic field with given, inertia degree, ramification index, discriminant, and ramification polygon. We then refine this formula further to the case where an additional invariant related to the residual polynomials of the segments of the ramification polygon is given.

Keywords

extension theorems fields

Cite

@article{arxiv.1512.06946,
  title  = {Counting Extensions of $\mathfrak{p}$-Adic Fields with Given Invariants},
  author = {Brian Sinclair},
  journal= {arXiv preprint arXiv:1512.06946},
  year   = {2015}
}

Comments

14 pages, 1 figure, 1 table. For additional tables, see http://www.uncg.edu/mat/numbertheory/tables/local/counting/. arXiv admin note: text overlap with arXiv:1504.06671

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