On Trace Forms of Algebraic Number Fields.
On Witt rings of function fields of real analytic surfaces and curves.
Let V be a paracompact connected real analytic manifold of dimension 1 or 2, i.e. a smooth curve or surface. We consider it as a subset of some complex analytic manifold VC of the same dimension. Moreover by a prime divisor of V we shall mean the irreducible germ along V of a codimension one subvariety of VC which is an invariant of the complex conjugation. This notion is independent of the choice of the complexification VC. In the one-dimensional case prime divisors are just points, in the two-dimensional...
On zeros of reciprocal polynomials of odd degree.
Ordered fields and sign-changing polynomials.
Ordres faibles et localisation de zéros de polynômes
Orthogonality and complementation in the lattice of subspaces of a finite vector space
We investigate the lattice of subspaces of an -dimensional vector space over a finite field with a prime power together with the unary operation of orthogonality. It is well-known that this lattice is modular and that the orthogonality is an antitone involution. The lattice satisfies the chain condition and we determine the number of covers of its elements, especially the number of its atoms. We characterize when orthogonality is a complementation and hence when is orthomodular. For...
Overdetermined Strata in General Families of Polynomials
2000 Mathematics Subject Classification: 12D10.In the paper we give different examples of overdetermined strata.
Pathological functions on Puiseux series ordered fields and others.
Piers Bohl stále inspirující
Článek je věnován památce Pierse Bohla (1865-1921), lotyšského matematika a šachisty, jehož mnohé výsledky předběhly svoji dobu a zůstaly tehdejší matematickou komunitou často nedoceněny. Kromě uvedení základních životopisných údajů komentuje tento text jeho dnes již všeobecně uznávaný přínos do několika oblastí matematické analýzy, zejména pak vět o pevném bodě a teorie kvaziperiodických funkcí. Hlavní inspirací pro sepsání tohoto článku byl však jiný Bohlův výsledek, tentokrát z oblasti teorie...
Polynomial cycles in algebraic number fields
Polynomials of the eigenvalues and powers of matrices
Polynomials with height 1 and prescribed vanishing at 1.
Positive polynomials and polynomial inequalities.
Préhistoire de la géométrie algébrique réelle : de Descartes à Tarski
Problème donné au concours général en 1874
Proof of the existence of certain triples of polynomials
Quadratic forms and radicals of fields
Quadratic Forms and the u-Invariant. I.
Quadratische Formen und die Artin-Schreiersche Theorie der formal reellen Körper
Quadratische Semi-Ordnungen und Quadratische Formen.