Prime Specialization in Higher Genus Ii
نویسنده
چکیده
We continue the development of the theory of higher-genus Möbius periodicity that was studied in Part I for odd characteristic, now treating asymptotic questions and the case of characteristic 2. The extra difficulties in characteristic 2 are overcome via rigid geometry in characteristic 0. The results on Möbius periodicity in any positive characteristic are used to incorporate a correction factor into the false naive conjecture of Bateman–Horn type concerning how often a polynomial with a higher-genus coefficient ring takes prime values; numerical evidence is provided to support the suitability of this correction factor. We also prove some asymptotic and non-triviality properties of the
منابع مشابه
Prime Specialization in Higher Genus I
A classical conjecture predicts how often a polynomial in Z[T ] takes prime values. The natural analogous conjecture for prime values of a polynomial f(T ) ∈ κ[u][T ], where κ is a finite field, is false. The conjecture over κ[u] was modified in earlier work by introducing a correction factor that encodes unexpected periodicity of the Möbius function at the values of f on κ[u] when f ∈ κ[u][T ]...
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تاریخ انتشار 2007