A Herbrand-Ribet theorem for function fields
نویسندگان
چکیده
منابع مشابه
A Modal Herbrand Theorem
We state and prove a modal Herbrand theorem that is, we believe, a more natural analog of the classical version than has appeared before. The statement itself requires the enlargement of the usual machinery of first-order modal logic — we use the device of predicate abstraction, something that has been considered elsewhere as well. This expands the expressive power of modal logic in a natural w...
متن کاملA Hidden Herbrand Theorem
3 Oxford Abstract. The beneets of the object, logic (or relational), functional, and constraint paradigms can be combined, by providing existential queries over objects and their attributes, subject to constraints. This paper provides a precise mathematical foundation for this novel programming paradigm, and shows that it is computationally feasible by reducing it to familiar problems over term...
متن کاملHermite’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 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.
متن کاملPrime Number Theorem for Algebraic Function Fields
Elementary proofs of the abstract prime number theorem of the form A(w) = qm + 0(qmm~i) for algebraic function fields are given. The proofs use a refinement of a tauberian theorem of Bombieri. 0. Introduction The main purpose of this paper is to give elementary proofs of the abstract prime number theorem for algebraic function fields (henceforth, the P.N.T.) which was established in the author'...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2011
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-011-0346-3