Weierstrass Points at the Cusps of Γ0(16p) and Hyperellipticity of Γ0(n)
1971 ◽
Vol 23
(6)
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pp. 960-968
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Keyword(s):
For a fixed positive integer n we consider the subgroup Γ0(n) of the modular group Γ(l). Γ0(n) consists of all linear fractional transformations L: z → (az + b)/(cz + d) with rational integers a, b, c, d, determinant ad – bc = 1, and c ≡ 0(mod n). If ℋ = {z|z = x + iy, x and y real and y > 0} is the upper half of the z-plane then S0 = S0(n) = ℋ/Γ0(n), properly compactified, is a compact Riemann surface whose genus we denote by g(n). A point P of a Riemann surface S of genus g is called a Weierstrass point if there exists a function on S that has a pole of order α ≦ g at P and is regular everywhere else on S.Lehner and Newman started the search for Weierstrass points of S0 (or, loosely, of Γ0(n)).
2009 ◽
Vol 05
(05)
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pp. 845-857
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Keyword(s):
1967 ◽
Vol 19
◽
pp. 268-272
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1978 ◽
Vol 21
(1)
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pp. 99-101
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1996 ◽
Vol 141
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pp. 79-105
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1973 ◽
Vol 14
(2)
◽
pp. 202-204
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Keyword(s):
1991 ◽
Vol 34
(1)
◽
pp. 67-73
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