# algebraic numbers

## Related Articles

- Some Results Connected with the Class Number Problem in Real Quadratic Fields. Grytczuk, Aleksander; Grytczuk, Jarosław // Acta Mathematica Sinica;Oct2005, Vol. 21 Issue 5, p1107
We investigate arithmetic properties of certain subsets of square-free positive integers and obtain in this way some results concerning the class number h( d) of the real quadratic field $$ \mathbb{Q}{\left( {{\sqrt d }} \right)} $$. In particular, we give a new proof of the result of Hasse,...

- WHITNEY'S EXTENSION PROBLEMS AND INTERPOLATION OF DATA. Fefferman, Charles // Bulletin (New Series) of the American Mathematical Society;Apr2009, Vol. 46 Issue 2, p207
Given a function f : E â†’ R with E âŠ‚ ℝ:n, we explain how to decide whether f extends to a âŠ‚m function F on â„n. If E is finite, then one can efficiently compute an F as above, whose Cm norm has the least possible order of magnitude (joint work with B. Klartag).

- Generalized Formal Degree. Qiu, Yannan // IMRN: International Mathematics Research Notices;Jan2012, Vol. 2012 Issue 2, p239
Let G be a reductive group over a local field of characteristic zero or a finite central cover of such a group. We present a conjecture that enables one to define formal degree for all unitary representations of G. The conjecture is proved for GLn and over real and p-adic fields, together with a...

- Polynomials with small discriminants and regular systems of real algebraic numbers. Bernik, V. I.; Kukso, O. S. // Journal of Mathematical Sciences;Aug2006, Vol. 137 Issue 2, p4612
The distribution of special algebraic numbers is studied, and an optimal regular system is constructed. Bibliography: 11 titles.

- Non uniform random generation of generalized Motzkin paths. Brlek, Srečko; Pergola, Elisa; Roques, Olivier // Acta Informatica;Apr2006, Vol. 42 Issue 8/9, p603
We consider in this paper the class M k n of generalized Motzkin paths of length n, that is, lattice paths using steps (1,1), (1,âˆ’1), ( k,0), where k is a fixed positive integer, starting at the origin (0,0), running above the x-axis, and ending at ( n,0). The area is the region bounded...

- On Archimedean Fields. Schleiermacher, Adolf // Journal of Geometry;2009, Vol. 92 Issue 1/2, p143
In this note we consider formally real fields that admit only of Archimedean orderings. Such fields will be called Archimedean. We establish necessary and sufficient conditions for a formally real field to be Archimedean. We also characterize in terms of convexity the positive cones of...

- The embedding problem with non-Abelian kernel for local fields. Ishkhanov, V.; Lur�e, B. // Journal of Mathematical Sciences;Sep2009, Vol. 161 Issue 4, p553
The embedding problem of local fields with p-groups is equivalent to its associated Abelian problem if the inequality d = r + 2 is valid; here d and r are the numbers of generators of the Demushkin group and of the Galois group of an embedded field. Bibliography: 6 titles.

- The cardinal coefficients of the Ideal $${{\mathcal {I}}_{f}}$$. Osuga, Noboru; Kamo, Shizuo // Archive for Mathematical Logic;Nov2008, Vol. 47 Issue 7/8, p653
In 2002, Yorioka introduced the s-ideal $${{\mathcal {I}}_f}$$ for strictly increasing functions f from ? into ? to analyze the cofinality of the strong measure zero ideal. For each f, we study the cardinal coefficients (the additivity, covering number, uniformity and cofinality) of $${{\mathcal...

- *-Extremal valued fields. Ershov, Yu. L. // Siberian Mathematical Journal;Nov2009, Vol. 50 Issue 6, p1007
We propose a convenient modification for the concept of extremal field which was introduced by the author previously and turned out to be degenerate.