An analogue of the prime number theorem for polynomials over night as well as its connection to the necklace factorization algorithm T-transform and the string complexity measure T-complexity are explored.Expand

A generalized form of Möbius inversion applies to the Lindelöf-Wirtinger expansion of the Lerch transcendent function and implies an inversion formula for the Hurwitz zeta function as a limiting case.Expand

For the classical Stirling numbers of the second kind, asymptotic formulae are derived in terms of a local central limit theorem. The underlying probabilistic approach also applies to the… Expand

These numbers are defined as the coefficients of the Euler–Frobenius polynomials which usually are introduced via the rational function expansion n being a nonnegative integer and λ∈[0, 1). The… Expand

By making use of some explicit relationships between the Apostol-Bernoulli, Apostol-Euler, Apostol-Genocchi, and Apostol-Frobenius-Euler polynomials of higher order and the generalized Hurwitz-Lerch… Expand

The author has found today an error in the denominator of the residue equation (4.5). This unfortunate mistake makes the conclusions and the title of the paper incorrect. The function $Z(s,x)$ is… Expand

As a first application of a very old theorem, known as Herschel's theorem, we provide direct elementary proofs of several explicit expressions for some numbers and polynomials that are known in… Expand