An improved estimate on the distribution mod 1 of powers of real matrices
An improved result on irregularities in distribution of sequences of integers
In 1972 the author used a result of K.F. Roth on irregularities in distribution of sequences of real numbers to prove an analogous result related to the distribution of sequences of integers in prescribed residue classes. Here, a 1972 result of W.M. Schmidt, which is an improvement of Roth's result, is used to obtain an improved result for sequences of integers.
An improved upper bound for G(k) in Waring's problem for relatively small k
An improved upper bound for the discrepancy of quadratic congruential pseudorandom numbers
An improved upper bound for the sum-free subset constant.
An improved upper bound on the maximum size of -primitive sets.
An improvement of an estimate for finite additive bases
An improvement of Euclid's algorithm
The paper introduces the calculation of a greatest common divisor of two univariate polynomials. Euclid’s algorithm can be easily simulated by the reduction of the Sylvester matrix to an upper triangular form. This is performed by using - transformation and -factorization methods. Both procedures are described and numerically compared. Computations are performed in the floating point environment.
An improvement of Lenstra's criterion for Euclidean number fields: The totally real case
An improvement of the quantitative subspace theorem
An improvement on Olson's constant for ℤₚ ⊕ ℤₚ
An improvement to Chalk's estimation of exponential sums
An inductive derivation of Stirling numbers of the second kind and their applications in statistics.
An inductive method for proving the transcendence of certain series
An inequality for Fibonacci numbers
We extend an inequality for Fibonacci numbers published by P. G. Popescu and J. L. Díaz-Barrero in 2006.
An inequality for local unitary Theta correspondence
Given a representation of a local unitary group and another local unitary group , either the Theta correspondence provides a representation of or we set . If is fixed and varies in a Witt tower, a natural question is: for which is ? For given dimension there are exactly two isometry classes of unitary spaces that we denote . For let us denote the minimal of the same parity of such that , then we prove that where is the dimension of .
An inequality for the class number.
An infinite dimensional Hodge-Tate theory
An infinite family of dual sequence identities.
An infinite family of elliptic curves over Q with large rank via Néron's method.