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GAPS IN TAYLOR SERIES OF ALGEBRAIC FUNCTIONS

Part of: Algebraic number theory: global fields Curves

Published online by Cambridge University Press:  26 February 2015

SETH DUTTER
SETH DUTTER*
Affiliation:
Department of Mathematics, Statistics and Computer Science, University of Wisconsin – Stout, Menomonie, WI 54751, USA email dutters@uwstout.edu
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Abstract

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Let $f$ be a rational function on an algebraic curve over the complex numbers. For a point $p$ and local parameter $x$ we can consider the Taylor series for $f$ in the variable $x$. In this paper we give an upper bound on the frequency with which the terms in the Taylor series have $0$ as their coefficient.

Keywords

algebraic functionsfunction fieldsTaylor series

MSC classification

Primary: 14H05: Algebraic functions; function fields
Secondary: 11R58: Arithmetic theory of algebraic function fields
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 3 , June 2015 , pp. 412 - 418
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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