Abc Implies No \siegel Zeros" for L-functions of Characters with Negative Discriminant
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منابع مشابه
Nonvanishing of quadratic Dirichlet L - functions at s
The Generalized Riemann Hypothesis (GRH) states that all non-trivial zeros of Dirichlet L-functions lie on the line Re(s) = 12 . Further, it is believed that there are no Q-linear relations among the non-negative ordinates of these zeros. In particular, it is expected that L( 1 2 , χ) 6= 0 for all primitive characters χ, but this remains still unproved. This appears to have been first conjectur...
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We give explicit lower bounds on the modular degree of a rational elliptic curve. The technique is via a convolution-type formula involving the symmetric-square L-function, for which an analogue of “no Siegel zeros” is known due to a result of Goldfeld, Hoffstein, and Lieman; our main task is to determine an explicit constant for their bound. Combined with an easy bound on the Faltings height i...
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تاریخ انتشار 2007