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...
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 field, to show that for every k, the irreducible polynomials in Fq[t] contain configurations of the form {f + P g : deg(P) < k}, g = 0.
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.
متن کاملA Generalization of Roth’s Theorem in Function Fields
Let Fq[t] denote the polynomial ring over the finite field Fq, and let SN denote the subset of Fq[t] containing all polynomials of degree strictly less than N . For non-zero elements r1, ⋅ ⋅ ⋅ , rs of Fq satisfying r1 + ⋅ ⋅ ⋅ + rs = 0, let Dr(SN ) denote the maximal cardinality of a set A ⊆ SN which contains no non-trivial solution of r1x1 + ⋅ ⋅ ⋅+ rsxs = 0 with xi ∈ A (1 ≤ i ≤ s). We prove tha...
متن کاملRudnick and Soundararajan's theorem for function fields
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: International Mathematics Research Notices
سال: 2013
ISSN: 1687-0247,1073-7928
DOI: 10.1093/imrn/rnt125