A higher weight analogue of Ogg’s theorem on Weierstrass points
Keyword(s):
For a positive integer [Formula: see text], we say that [Formula: see text] is a Weierstrass point on the modular curve [Formula: see text] if there is a non-zero cusp form of weight [Formula: see text] on [Formula: see text] which vanishes at [Formula: see text] to order greater than the genus of [Formula: see text]. If [Formula: see text] is a prime with [Formula: see text], Ogg proved that [Formula: see text] is not a Weierstrass point on [Formula: see text] if the genus of [Formula: see text] is [Formula: see text]. We prove a similar result for even weights [Formula: see text]. We also study the space of weight [Formula: see text] cusp forms on [Formula: see text] vanishing to order greater than the dimension.
1985 ◽
Vol 98
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pp. 117-137
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2015 ◽
Vol 152
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pp. 223-254
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1971 ◽
Vol 23
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pp. 960-968
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1984 ◽
Vol 25
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pp. 107-119
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2014 ◽
Vol 11
(01)
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pp. 39-49
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2014 ◽
Vol 10
(08)
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pp. 1921-1927
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2014 ◽
Vol 15
(3)
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pp. 471-510
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1984 ◽
Vol 93
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pp. 149-171
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