منابع مشابه
Totally Ramified Primes and Eisenstein Polynomials
is Eisenstein at a prime p when each coefficient ci is divisible by p and the constant term c0 is not divisible by p 2. Such polynomials are irreducible in Q[T ], and this Eisenstein criterion for irreducibility is the way nearly everyone first meets Eisenstein polynomials. Here, we will show Eisenstein polynomials are closely related to total ramification of primes in number fields. Let K be a...
متن کاملGeometry of Hilbert Modular Varieties over Totally Ramified Primes
Let L be a totally real field with ring of integers OL. Let N ≥ 4 be an integer and let M(μN) be the fine moduli scheme over Z of polarized abelian varieties with real multiplication (RM) and μN-level structure, satisfying the Deligne-Pappas condition. For every scheme S, we let M(S, μN) = M(μN) ×Z S be the moduli scheme over S; see Definition 2.1. Many aspects of the geometry of the modular va...
متن کاملd-VFCSR or vectorial FCSR constructed on totally ramified extension of the p-adic numbers
In this paper, we introduce a vectorial conception of dFCSRs to build these registers over any finite field. We describe the structure of d-vectorial FCSRs and we develop an analysis to obtain basic properties like periodicity and the existence of maximal length sequences. To illustrate these vectorial d-FCSRs, we present simple examples and we compare with those of Goresky, Klapper and Xu.
متن کاملSingular values of multiple eta-quotients for ramified primes
We determine the conditions under which singular values of multiple η-quotients of square-free level, not necessarily prime to 6, yield class invariants, that is, algebraic numbers in ring class fields of imaginary-quadratic number fields. We show that the singular values lie in subfields of the ring class fields of index 2 ′ −1 when k > 2 primes dividing the level are ramified in the imaginary...
متن کاملZETA FUNCTIONS OF TOTALLY RAMIFIED p-COVERS OF THE PROJECTIVE LINE
In this paper we prove that there exists a Zariski dense open subset U defined over the rationals Q in the space of all one-variable rational functions with arbitrary l poles of prescribed orders, such that for every geometric point f in U(Q), the L-function of the exponential sum of f at a prime p has Newton polygon approaching the Hodge polygon as p approaches infinity. As an application to a...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1976
ISSN: 0040-8735
DOI: 10.2748/tmj/1178240839