DOIAbstract
AbstractIn this paper we obtain an improved asymptotic formula on the frequency of k-free numbers with a given difference. We also give a new upper bound of Barban–Davenport–Halberstam type for the k-free numbers in arithmetic progressions
AbstractIn this paper we obtain an improved asymptotic formula on the frequency of k-free numbers with a given difference. We also give a new upper bound of Barban–Davenport–Halberstam type for the k-free numbers in arithmetic progressions
By means of finite differences and partial fraction decomposition, we establish two binomial transfo...
AbstractA new expansion is given for partial sums of Eulerʼs pentagonal number series. As a corollar...
AbstractThe main purpose of this paper is using a mean value theorem of Dirichlet L-functions to stu...
AbstractAs a generalization of Calkin's identity and its alternating form, we compute a kind of bino...
AbstractUsing the WZ-method we find some of the easiest Ramanujan's formulae and also some new inter...
AbstractWe present several congruences for sums of the type ∑k=1p−1mkk−r(2kk)−1, modulo a power of a...
Contains a correction with respect to the printed versionWe provide sharp estimates for the number o...
AbstractWe find an enumeration formula for a (t,q)-Euler number which is a generalization of the q-E...
AbstractLet m,n≥2, m≤n. It is well-known that the number of (two-dimensional) threshold functions on...
AbstractBy applying the duplicate form of Carlitz inversions to three special cases of the q-Saalsch...
AbstractThis note is a continuation of a paper by the same authors that appeared in 2002 in the same...
AbstractIt is known that∑k=0∞(2kk)(2k+1)4k=π2and∑k=0∞(2kk)(2k+1)16k=π3. In this paper we obtain thei...
AbstractWe present some variations on the Greene–Krammerʼs identity which involve q-Catalan numbers....
AbstractWe obtain an asymptotic formula for the number of square-free values among p−1, for primes p...
AbstractLet N be sufficiently large odd integer. It is proved that the equation N=n1+n2+n3 has solut...
By means of finite differences and partial fraction decomposition, we establish two binomial transfo...
AbstractA new expansion is given for partial sums of Eulerʼs pentagonal number series. As a corollar...
AbstractThe main purpose of this paper is using a mean value theorem of Dirichlet L-functions to stu...
AbstractAs a generalization of Calkin's identity and its alternating form, we compute a kind of bino...
AbstractUsing the WZ-method we find some of the easiest Ramanujan's formulae and also some new inter...
AbstractWe present several congruences for sums of the type ∑k=1p−1mkk−r(2kk)−1, modulo a power of a...
Contains a correction with respect to the printed versionWe provide sharp estimates for the number o...
AbstractWe find an enumeration formula for a (t,q)-Euler number which is a generalization of the q-E...
AbstractLet m,n≥2, m≤n. It is well-known that the number of (two-dimensional) threshold functions on...
AbstractBy applying the duplicate form of Carlitz inversions to three special cases of the q-Saalsch...
AbstractThis note is a continuation of a paper by the same authors that appeared in 2002 in the same...
AbstractIt is known that∑k=0∞(2kk)(2k+1)4k=π2and∑k=0∞(2kk)(2k+1)16k=π3. In this paper we obtain thei...
AbstractWe present some variations on the Greene–Krammerʼs identity which involve q-Catalan numbers....
AbstractWe obtain an asymptotic formula for the number of square-free values among p−1, for primes p...
AbstractLet N be sufficiently large odd integer. It is proved that the equation N=n1+n2+n3 has solut...
By means of finite differences and partial fraction decomposition, we establish two binomial transfo...
AbstractA new expansion is given for partial sums of Eulerʼs pentagonal number series. As a corollar...
AbstractThe main purpose of this paper is using a mean value theorem of Dirichlet L-functions to stu...
Add to ORKG