Cubic function fields with prescribed ramification
نویسندگان
چکیده
منابع مشابه
Hilbert Modular Forms with Prescribed Ramification
Let K be a totally real field. In this article we present an asymptotic formula for the number of Hilbert modular cusp forms f with given ramification at every place v of K. The meaning of “given ramification” needs to be made clear: when v is an infinite place, it means specifying the weight of f at k, and when v is finite, it means specifying the restriction to inertia of the local Weil-Delig...
متن کاملPurely Cubic Function Fields With Short Periods
A “function field version” of Voronoi’s algorithm can be used to compute the fundamental unit of a purely cubic complex congruence function field of characteristic at least 5. This is accomplished by generating a sequence of minima in the maximal order of the field. The number of mimima computed is the period of the field. Generally, the period is very large — it is proportional to the regulato...
متن کاملRamification of Local Fields with Imperfect Residue Fields II
In [1], a filtration by ramification groups and its logarithmic version are defined on the absolute Galois group of a complete discrete valuation field without assuming that the residue field is perfect. In this paper, we study the graded pieces of these filtrations and show that they are abelian except possibly in the absolutely unramified and non-logarithmic case. 2000 Mathematics Subject Cla...
متن کاملRamification of local fields with imperfect residue fields I
Let K be a complete discrete valuation field, and let G be the Galois group of a separable closure Ω. Classically the ramification filtration of G is defined in the case where the residue field of K is perfect ([5], Chapter IV). In this paper, we define without any assumption on the residue field, two ramification filtrations of G and study some of their properties. Our first filtration, (G)a∈Q...
متن کاملTabulation of cubic function fields via polynomial binary cubic forms
We present a method for tabulating all cubic function fields over Fq(t) whose discriminant D has either odd degree or even degree and the leading coefficient of −3D is a non-square in Fq , up to a given bound B on deg(D). Our method is based on a generalization of Belabas’ method for tabulating cubic number fields. The main theoretical ingredient is a generalization of a theorem of Davenport an...
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: International Journal of Number Theory
سال: 2021
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042121500755