Parity of Class Numbers and Witt Equivalence of Quartic Fields
نویسندگان
چکیده
منابع مشابه
Witt Equivalence Classes of Quartic
It has recently been established that there are exactly seven Witt equivalence classes of quadratic number fields, and then all quadratic and cubic number fields have been classified with respect to Witt equivalence. In this paper we have classified number fields of degree four. Using this classification, we have proved the Conjecture of Szymiczek about the representability of Witt equivalence ...
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as x → ∞, where L(x) is the function L(x) = ∫ x 1 e t dt. Sarnak established this result by identifying the regulators with lengths of closed geodesics of the modular curve SL2(Z)\H, where H denotes the upper half-plane, and using the Prime Geodesic Theorem for this Riemannian surface. Actually Sarnak proved not this result but the analogue where h(O) is replaced by the class number in the narr...
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Witt equivalent fields can be understood to be fields having the same symmetric bilinear form theory. Witt equivalence of finite fields, local fields and global fields is well understood. Witt equivalence of function fields of curves defined over archimedean local fields is also well understood. In the present paper, Witt equivalence of general function fields over global fields is studied. It ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1995
ISSN: 0025-5718
DOI: 10.2307/2153380