Definite lattices over real algebraic function domains

1985 ◽  
Vol 272 (4) ◽  
pp. 461-475 ◽  
Author(s):  
H. -G. Quebbemann
Keyword(s):  
Algebraic Function ◽  
Real Algebraic Function

scholarly journals On existence of tame Harrison map

2007 ◽  
Vol 57 (5) ◽  
Author(s):  
Przemysław Koprowski
Keyword(s):  
Class Group ◽  
Function Fields ◽  
Algebraic Function ◽  
The Other ◽  
Closed Field ◽  
Group Isomorphism ◽  
Witt Rings ◽  
Algebraic Function Fields ◽  
New Criteria ◽  
Real Algebraic Function

AbstractWe present here two new criteria for existence of a tame Harrison map of two formally real algebraic function fields over a fixed real closed field of constants. The first criterion (c.f. Theorem 2.5) shows that a square class group isomorphism is a tame Harrison map if it induces an isomorphism of the coproduct rings of residue Witt rings. The other result (c.f. Proposition 3.5) associates a tame Harrison map to an integral quaternion-symbol equivalence.

Polynomial beta functions

1994 ◽  
Vol 14 (3) ◽  
pp. 453-474 ◽  
Author(s):  
Valerio De Angelis
Keyword(s):  
Spectral Radius ◽  
Algebraic Function ◽  
Beta Function ◽  
Complex Numbers ◽  
Algebraic Integers ◽  
Change Of Variables ◽  
Necessary And Sufficient ◽  
Positive Complex

AbstractThe pointwise spectral radii of irreducible matrices whose entries are polynomials with positive, integral coefficients are studied in this paper. Most results are derived in the case that the resulting algebraic function, the beta function of S. Tuncel, is in fact a polynomial. We show that the set of beta functions forms a semiring, and the spectral radius of a matrix of beta functions is again a beta function. We also show that the coefficients of a polynomial beta function p must be real algebraic integers, and p satisfies (after a change of variables if necessary) the inequality for non-zero (and not all positive) complex numbers z1,…,zd. If and the ordered sequence of exponents appearing in p is of the form (m,m+1,…,M−,1,M) for some integers m and M, the same inequality is necessary and sufficient for p to be a beta function.

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