ON THE VANISHING OF FOURIER COEFFICIENTS OF CERTAIN GENUS ZERO NEWFORMS
2011 ◽
Vol 07
(05)
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pp. 1229-1245
Keyword(s):
Given a classical modular form f(z), a basic question is whether any of its Fourier coefficients vanish. This question remains open for certain modular forms. For example, let Δ(z) = ΣΓ(n)qn ∈ S12(Γ0(1)). A well-known conjecture of Lehmer asserts that τ(n) ≠ 0 for all n. In recent work, Ono constructed a family of polynomials An(x) ∈ ℚ[x] with the property that τ(n) vanishes if and only if An(0) and An(1728) do. In this paper, we establish a similar criterion for the vanishing of coefficients of certain newforms on genus zero groups of prime level.
2010 ◽
Vol 06
(01)
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pp. 69-87
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2006 ◽
Vol 49
(4)
◽
pp. 526-535
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2002 ◽
Vol 65
(2)
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pp. 239-252
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2007 ◽
Vol 326
(1)
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pp. 655-666
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2011 ◽
Vol 07
(04)
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pp. 1065-1074
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2019 ◽
Vol 15
(05)
◽
pp. 907-924
Keyword(s):
2009 ◽
Vol 05
(08)
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pp. 1433-1446
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