Biquaternion algebras and quartic extensions
Birational geometry of quadrics
We construct new birational maps between quadrics over a field. The maps apply to several types of quadratic forms, including Pfister neighbors, neighbors of multiples of a Pfister form, and half-neighbors. One application is to determine which quadrics over a field are ruled (that is, birational to the projective line times some variety) in a larger range of dimensions. We describe ruledness completely for quadratic forms of odd dimension at most 17, even dimension at most 10, or dimension 14....
Birational transformations and values of the Riemann zeta-function
In his proof of Apery’s theorem on the irrationality of , Beukers [B] introduced double and triple integrals of suitable rational functions yielding good sequences of rational approximations to and . Beukers’ method was subsequently improved by Dvornicich and Viola, by Hata, and by Rhin and Viola. We give here a survey of our recent results ([RV2] and [RV3]) on the irrationality measures of and based upon a new algebraic method involving birational transformations and permutation groups...
Bloch and Kato's exponential map: three explicit formulas.
Block additive functions on the Gaussian integers
Block Factorization of Hankel Matrices and Euclidean Algorithm
It is shown that a real Hankel matrix admits an approximate block diagonalization in which the successive transformation matrices are upper triangular Toeplitz matrices. The structure of this factorization was first fully discussed in [1]. This approach is extended to obtain the quotients and the remainders appearing in the Euclidean algorithm applied to two polynomials u(x) and v(x) of degree n and m, respectively, whith m < ...
Block systems of a Galois group.
Block uniform distribution of random sequences. (Blockgleichverteilung von Zufallszahlenfolgen.)
Blocks and progressions in subset sum sets
Blocks for symmetric groups and their covering groups and quadratic forms.
Bohr local properties of
Bombieri's theorem in short intervals
Bombieri's theorem in short intervals. II.
Bombieri-Vinogradov type theorems for sparse sets of moduli
Borne polynomiale pour le nombre de points rationnels des courbes
Soit un polynôme en deux variables, de degré et à coefficients entiers dans pour . Alors le nombre de zéros rationnels de est soit infini soit plus petit que . Nous montrons aussi une version plus générale sur les corps de nombres.
Bornes effectives pour certaines fonctions concernant les nombres premiers
Si est le k nombre premier, la fonction de Chebyshev. Nous obtenons de nouvelles estimations et des améliorations des bornes données par Rosser et Schoenfeld, Schoenfeld et Robin pour les fonctionsCes estimations sont obtenues en utilisant des méthodes basées sur l’intégrale de Stieltjes et par calcul direct pour les petites valeurs.
Borwein and Bradley's Apéry-like formulae for .
Boundary cohomology of Shimura varieties. I. Coherent cohomology on toroidal compactifications
Boundary cohomology of Shimura varieties, II. Hodge theory at the boundary (Erratum).
Boundary cohomology of Shimura varieties. II. Hodge theory at the boundary.