The Real Holomorphy Ring and Sums of Powers in Rational and Elliptic Function Fields over The Field of Real Numbers
نویسندگان
چکیده
This thesis is devoted to a study of real holomorphy rings in R(x) and elliptic function fields R(x)( √ 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 fields R(x) and then investigate their extension to elliptic function fields 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 fields and finally we study applications to sums of powers.
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