Browsing by Author "Hunde, Natea"

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    The Real Holomorphy Ring and Sums of Powers in Rational and Elliptic Function Fields Over the Field of Real Numbers
    (Addis Ababa University, 2017-03) Hunde, Natea; Becker, Eberhard (PhD)
    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.