A combinatorial interpretation of the poly-Bernoulli numbers and two Fermat analogues.
A congruence involving the quotients of Euler and its applications (I)
A congruence involving the quotients of Euler and its applications (II)
A different -analogue of Euler numbers. (Un autre -analogue des nombres d'Euler.)
A Disproof of a Conjecture of Robertson and Generalizations
A generalization of the Bernoulli polynomials.
A generalization of the Lerch-Mordell formulas for positive discriminants
A generalization of the reciprocity law of multiple Dedekind sums
Various multiple Dedekind sums were introduced by B.C.Berndt, L.Carlitz, S.Egami, D.Zagier and A.Bayad.In this paper, noticing the Jacobi form in Bayad [4], the cotangent function in Zagier [23], Egami’s result on cotangent functions [14] and their reciprocity laws, we study a special case of the Jacobi forms in Bayad [4] and deduce a generalization of Egami’s result on cotangent functions and a generalization of Zagier’s result. Further, we consider their reciprocity laws.
A mean value theorem on differences of two k-th powers of numbers in residue classes.
A new approach to -Bernoulli numbers and -Bernoulli polynomials related to -Bernstein polynomials.
A new generating function of (-) Bernstein-type polynomials and their interpolation function.
A new -analogue of Bernoulli polynomials associated with -adic -integrals.
A note about the sums of products of Bernoulli numbers.
A Note on Bernoulli numbers and polynomials.
A note on Euler number and polynomials.
A note on Nörlund-type twisted -Euler polynomials and numbers of higher order associated with fermionic invariant -integrals.
A note on symmetric properties of the twisted -Bernoulli polynomials and the twisted generalized -Bernoulli polynomials.
A note on the -extension of Bernoulli numbers and Bernoulli polynomials.
A Note on the Hurwitz Zeta Function
A note on the multiple twisted Carlitz's type -Bernoulli polynomials.