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Zbl 0839.12005
Caragiu, Mihai
On the combinatorics of squares in some zero characteristic fields.
[J] Nieuw Arch. Wiskd., IV. Ser. 13, No.2, 209-218 (1995). ISSN 0028-9825

Guided by the difficult problem of specific connections between the distribution of squares in the rationals and congruent numbers, the author uses analogous results by {\it H. Davenport} [J. Lond. Math. Soc. 8, 46-52 (1933; Zbl 0006.24901)] for finite fields to devise a class of infinite fields in which the combinatorics of squares is ``unrestricted.'' Basic properties of ultraproducts are exploited in the development; e.g., Łos' fundamental theorem. Extensions to higher power residues are discussed.
[A.A.Mullin (Huntsville)]
MSC 2000:
*12L10 Ultraproducts in field theory
03C20 Ultraproducts and related constructions

Keywords: infinite fields; elliptic curves; ultraproducts

Citations: Zbl 0006.24901

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