I fondamenti di Zolotarev della teoria dei numeri algebrici
Icosahedral Galois Extensions and Elliptic Curves.
Ideal arithmetic and infrastructure in purely cubic function fields
This paper investigates the arithmetic of fractional ideals of a purely cubic function field and the infrastructure of the principal ideal class when the field has unit rank one. First, we describe how irreducible polynomials decompose into prime ideals in the maximal order of the field. We go on to compute so-called canonical bases of ideals; such bases are very suitable for computation. We state algorithms for ideal multiplication and, in the case of unit rank one and characteristic at least five,...
Ideal class group annihilators
Ideal class groups, Hilbert’s irreducibility theorem, and integral points of bounded degree on curves
We study the problem of constructing and enumerating, for any integers , number fields of degree whose ideal class groups have “large" -rank. Our technique relies fundamentally on Hilbert’s irreducibility theorem and results on integral points of bounded degree on curves.
Ideal Class Groups in Basic ...p1 x....x...ps-Extensions of Abelian Number Fields.
Ideal class groups of cubic cyclic fields
Ideal class groups of cyclotomic number fields I
Ideal class groups of cyclotomic number fields II
Ideal class groups of cyclotomic number fields III
Ideal Criteria for both Ideal Criteria for both X2-dy2 = M1 And X2-dy2 = M2 to have Primitive Solutions for any Integers M1, M2 Prime to D > 0
This article provides necessary and sufficient conditions for both of the Diophantine equations X^2 − DY^2 = m1 and x^2 − Dy^2 = m2 to have primitive solutions when m1 , m2 ∈ Z, and D ∈ N is not a perfect square. This is given in terms of the ideal theory of the underlying real quadratic order Z[√D].
Ideal Matrices and Ideal Vectors.
Ideal version of Ramsey's theorem
We consider various forms of Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem which are connected with ideals of subsets of natural numbers. We characterize ideals with properties considered. We show that, in a sense, Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem characterize the same class of ideals. We use our results to show some versions of density Ramsey's theorem (these are similar to generalizations shown in [P....
Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung.
Ideals in the semiring N
Ideals not prime to the conductor in quadratic orders
Ideal-theoretic characterization of the relative genus field.
Idéaux de fonctions analytiques bornées stables par dérivation
Idele characters in spectral synthesis on
Let , . We construct Dirichlet series where for each fixed in a half plane, , as a function of , is a non-synthesizable absolutely convergent Fourier series. Because of the way the frequencies in are chosen, we are motivated to introduce a class of synthesizable absolutely convergent Fourier series which are defined in terms of idele characters. We solve the “problem of analytic continuation” in this setting by constructing pseudo-measures, determined by idele characters, when .
Identically distributed pairs of partition statistics.