Currently, all major implementations of cyclotomic fields as well as number fields, are based on a dense model where elements are represented either as dense polynomials in the generator of the field or as coefficient vectors with respect to a fixed basis. While this representation allows for the asymptotically fastest arithmetic for general elements, it is unsuitable for fields of degree > 10 ...

Let F ′/F be a finite normal extension of number fields with Galois group Gal(F ′/F ). Let χ be an irreducible character of Gal(F ′/F ) of degree greater than one and L(s, χ) the associated Artin L-function. Assuming the truth of Artin’s conjecture, we have explicitly determined a zero-free region about 1 for L(s, χ). As an application we show that, for a CM-field K of degree 2n with solvable n...

In the present paper we show that a stem finite p -group G has size bounded by min ⁡ ( 8 d − 2 log + b 4 ) 1 / , 3 where is breadth of and maximum character degree . As consequence there are only finitely many -groups having

We review here the difference between quantum statistical treatments and semiclassical ones, using as the main concomitant tool a semiclassical, shift-invariant Fisher information measure built up with Husimi distributions. Its semiclassical character notwithstanding, this measure also contains abundant information of a purely quantal nature. Such a tool allows us to refine the celebrated Lieb ...

In this paper, we redefine the sample points set in the feature space from the point of view of weighted graph and propose a new covering model — Multi-Degree-of-Freedom Neurons (MDFN). Base on this model, we describe a geometric learning algorithm with 3-degree-offreedom neurons. It identifies the sample points set’s topological character in the feature space, which is different from the tradi...

Abstract The COBE satellite’s maps of the cosmic microwave background (CMB) anisotropy do not have the resolution to discriminate between theories of cosmic structure formation based on inflation, and those based on field ordering following a symmetry breaking phase transition. For this purpose it is critical to resolve the CMB anisotropy on degree scales. In this paper we report on detailed ca...

A course of medical education for the MD degree ordinarily consists of a minimum of four years of study. Students recommended for the Doctor of Medicine degree must be of good moral character, they must have completed an entire academic course of instruction as matriculated medical students, they must have passed all required subjects or the equivalent and have received satisfactory grades in t...

Let G be a finite group and let cd(G) be the set of irreducible character degrees of G. The degree graph ∆(G) is the graph whose set of vertices is the set of primes that divide degrees in cd(G), with an edge between p and q if pq divides a for some degree a ∈ cd(G). We determine the graph ∆(G) for the finite simple groups of types A`(q) and A`(q ), that is, for the simple linear and unitary gr...

The aim of this paper is to explain how, starting from a Goppa code C(X,G, P1, ..., Pn) and a cyclic covering π : Y → X of degree m, one can twist the initial code to another one C(X,G + Dχ, P1, ..., Pn), where Dχ is a non-principal degree 0 divisor on X associated to a character χ of Gal(Y/X), in the hope that `X(G + Dχ) > `X(G). We give, using a MAGMA program, several examples where this occu...