منابع مشابه
Hermite’s Theorem for Function Fields
Hermite’s theorem states that there are only finitely many number fields with bounded discriminant. In this work, we investigate an analog of Hermite’s theorem for function fields: there are only finitely many separable function fields with bounded degree and discriminant. We prove this in the case that the function fields are unramified at ∞. Although Hermite’s theorem for function fields is k...
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متن کاملGreen-tao Theorem in Function Fields
We adapt the proof of the Green-Tao theorem on arithmetic progressions in primes to the setting of polynomials over a finite fields, to show that for every k, the irreducible polynomials in Fq[t] contains configurations of the form {f + P g : deg(P) < k}, g = 0.
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In this paper we prove a function field version of a theorem by Rudnick and Soundararajan about lower bounds for moments of quadratic Dirichlet L–functions. We establish lower bounds for the moments of quadratic Dirichlet L–functions associated to hyperelliptic curves of genus g over a fixed finite field Fq in the large genus g limit.
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2011
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa147-2-3