Determinant expressions for -harmonic congruences and degenerate Bernoulli numbers.
Diagonal checker-jumping and Eulerian numbers for color-signed permutations.
Diophantine equations with Bernoulli polynomials
Diophantine equations with Euler polynomials
We determine decomposition properties of Euler polynomials and using a strong result relating polynomial decomposition and diophantine equations in two separated variables, we characterize those g(x) ∈ ℚ [x] for which the diophantine equation with k ≥ 7 may have infinitely many integer solutions. Apart from the exceptional cases we list explicitly, the equation has only finitely many integer solutions.
Distribution of irregular pairs
Dynamical zeta functions and Kummer congruences
Ein Würfelschnittproblem und Bernoullische Zahlen.
Errata to the papers : “Connections between for even quadratic Dirichlet characters ” and “Class numbers of appropriate imaginary quadratic fields, parts I and II”
Euler numbers and polynomials associated with zeta functions.
Euler polynomials and the related quadrature rule.
Euler sums with Dirichlet characters
Eulerian numbers, Foulkes characters and Lefschetz characters of the symmetric group.
Eulerian numbers with fractional order parameters.
Evaluation of two trigonometric sums
Existence and reduction of generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials
One can find in the mathematical literature many recent papers studying the generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials, defined by means of generating functions. In this article we clarify the range of parameters in which these definitions are valid and when they provide essentially different families of polynomials. In particular, we show that, up to multiplicative constants, it is enough to take as the “main family” those given by and as an “exceptional family”...
Explicit formulas for Bernoulli and Euler numbers.
Explicit inverse of the Pascal matrix plus one.
Exploring the -Riemann zeta function and -Bernoulli polynomials.
Fermat and Wilson quotients for -adic integers
Fourier expansions and integral representations for Genocchi polynomials.