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

Published online by Cambridge University Press:  27 May 2014

ARUL SHANKAR
Affiliation:
Harvard University, Department of Mathematics, One Oxford Street, Cambridge, MA 02138, USA; [email protected]
JACOB TSIMERMAN
Affiliation:
Harvard University, Department of Mathematics, One Oxford Street, Cambridge, MA 02138, USA; [email protected]

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.

Type
Research Article
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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