Nonvanishing of hyperelliptic zeta functions over finite fields.
ALGEBRA & NUMBER THEORY(2020)
摘要
Fixing t is an element of R and a finite field F-q of odd characteristic, we give an explicit upper bound on the proportion of genus g hyperelliptic curves over F-q whose zeta function vanishes at 1/2 + it. Our upper bound is independent of g and tends to 0 as q grows.
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关键词
nonvanishing,L-functions,function fields,Dirichlet characters
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