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Zeros of Eisenstein series, quadratic class numbers and supersingularity for rational function fields

✍ Scribed by Gunther Cornelissen


Publisher
Springer
Year
1999
Tongue
English
Weight
174 KB
Volume
314
Category
Article
ISSN
0025-5831

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Class numbers of quadratic fields, Hasse
✍ John Brillhart; Patrick Morton πŸ“‚ Article πŸ“… 2004 πŸ› Elsevier Science 🌐 English βš– 389 KB

Using the theory of elliptic curves, we show that the class number hðÀpÞ of the field QΓ° ffiffiffiffiffiffi ffi Γ€p p Þ appears in the count of certain factors of the Legendre polynomials P m Γ°xÞ Γ°mod pÞ; where p is a prime 43 and m has the form Γ°p Γ€ eÞ=k; with k ΒΌ 2; 3 or 4 and p e Γ°mod kÞ: As part