The Real Holomorphy Ring and Sums of Powers in Rational and Elliptic Function Fields Over the Field of Real Numbers
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Date
2017-03
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Addis Ababa University
Abstract
This thesis is devoted to a study of real holomorphy rings in R(x) and elliptic
function _elds R(x)(p
f(x)); f is a monic polynomial of degree 3 with no
multiple roots in C over R and sums of powers in R(x). The objects of study
are real valuation rings, real holomorphy rings and real places in the rational
function _elds R(x) and then investigate their extension to elliptic function
_elds which are quadratic extension of R(x). We write down the full list of
real valuation rings to give the description of holomorphy ring in both _elds
and _nally we study applications to sums of powers.
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The Real Holomorphy Ring and Sums