A generalization of the binomial interpolated operator and its action on linear recurrent sequences.
A generalization of the classical circle problem
A generalization of the Lerch-Mordell formulas for positive discriminants
A generalization of the question of Sierpiński on geometric progressions.
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 generalized formula of Hardy.
A generalized recurrence for Bell numbers.
A generating functions proof of a curious identity.
A Kummer criterion for imaginary quadratic fields
A Linear Algorithm for Construction of Optimal Digital Convex 2k-gons
A matrix dynamics approach to Golomb's recursion.
A mean value density theorem of additive number theory
A mean value theorem on differences of two k-th powers of numbers in residue classes.
A multiple set version of the 3k-3 theorem.
A natural extension of Catalan numbers.
A natural prime-generating recurrence.
A new approach to -Bernoulli numbers and -Bernoulli polynomials related to -Bernstein polynomials.
A new class of -Fibonacci polynomials.
A new domino tiling sequence.
A new family of Somos-like recurrences.