At least 77% of Artin L-functions for D4-quartic function fields are non-vanishing at s=1/2 when ordered by conductor.
Nonvanishing of hyperelliptic zeta functions over finite fields
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Non-vanishing of Artin $L$-functions associated with $D_4$-quartic function fields ordered by conductor
At least 77% of Artin L-functions for D4-quartic function fields are non-vanishing at s=1/2 when ordered by conductor.