On the order of vanishing of the cyclotomic p-adic L-function

Details On the order of vanishing of the cyclotomic p-adic L-function On the order of vanishing of the cyclotomic p-adic L-function

2009-05-28

arxiv.org/abs/0905.4682v2

Mathematics

Number Theory

19 pages

Scientific paper

For a newform for Gamma_0(N) of even weight k, we prove that its attached
p-adic L-function is not identically zero on the group Z_p of the p-adic units.
If p >3, we prove that the order of vanishing at any p-adic integer is finite.

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