Binary Kloosterman sums using Stickelberger's theorem and the Gross-Koblitz formula
Binary linear forms over finite sets of integers
Binary Quadratic Discriminants with a Single Class of Forms in Each Genus
Binary quadratic forms and Eichler orders
For any Eichler order of level in an indefinite quaternion algebra of discriminant there is a Fuchsian group and a Shimura curve . We associate to a set of binary quadratic forms which have semi-integer quadratic coefficients, and we develop a classification theory, with respect to , for primitive forms contained in . In particular, the classification theory of primitive integral binary quadratic forms by is recovered. Explicit fundamental domains for allow the characterization...
Binary quadratic forms and sums of triangular numbers
Binary quadratic forms and the Fourier coefficients of elliptic and Jacobi modular forms.
Binary relations on the power set of an -element set.
Binomial coefficient predictors.
Binomial expansions modulo prime powers.
Binomial expected values of arithmetical functions.
Binomial squares in pure cubic number fields
Let , with a positive integer, be a pure cubic number field. We show that the elements whose squares have the form for rational numbers form a group isomorphic to the group of rational points on the elliptic curve . This result will allow us to construct unramified quadratic extensions of pure cubic number fields .
Binomial sums via Bailey's cubic transformation
By employing one of the cubic transformations (due to W. N. Bailey (1928)) for the -series, we examine a class of -series. Several closed formulae are established by means of differentiation, integration and contiguous relations. As applications, some remarkable binomial sums are explicitly evaluated, including one proposed recently as an open problem.
Binomial Thue's equation over function fields
Binomial-Coefficient Multiples of Irrationals.
Binomials transformation formulae for scaled Fibonacci numbers
The aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined by Wituła and Słota. The paper contains some original relations connecting the values of delta-Fibonacci numbers with the respective values of Chebyshev polynomials of the first and second kind.
Bioctic Gauss sums and sixteenth power residue difference sets
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.