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COUNTING $S_5$ -FIELDS WITH A POWER SAVING ERROR TERM

Part of: Differential algebra Rings and algebras with additional structure

Published online by Cambridge University Press:  27 May 2014

ARUL SHANKAR  and
JACOB TSIMERMAN
ARUL SHANKAR
Affiliation:
Harvard University, Department of Mathematics, One Oxford Street, Cambridge, MA 02138, USA; arul.shnkr@gmail.com
JACOB TSIMERMAN
Affiliation:
Harvard University, Department of Mathematics, One Oxford Street, Cambridge, MA 02138, USA; arul.shnkr@gmail.com

Abstract

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We show how the Selberg $\Lambda ^2$ -sieve can be used to obtain power saving error terms in a wide class of counting problems which are tackled using the geometry of numbers. Specifically, we give such an error term for the counting function of $S_5$ -quintic fields.

MSC classification

Secondary: 13N15: Derivations 16W55: “Super” (or “skew”) structure

Information

Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 2 , 01 July 2014 , e13
Creative Commons
Creative Common License - CCCreative Common License - BY
The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence .
Copyright
© The Author(s) 2014

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