An identity involving Ramanujan's sum.
An identity Ramanujan probably missed
"Ramanujan's 6-10-8 identity" inspired Hirschhorn to formulate his "3-7-5 identity". Now, we give a new "6-14-10 identity" which we suppose Ramanujan would have discovered but missed to mention in his notebooks.
An implementation of the number field sieve.
An improved algorithm for the solution of integer programs by the solution of associated diophantine equations
An Improved Bound for Prime Solutions of Some Ternary Equations.
An improved estimate concerning 3n+1 predecessor sets
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