Über eine besondere Dirchletsche Reihe.

@article{WirtingerberEB,
  title={{\"U}ber eine besondere Dirchletsche Reihe.},
  author={Wilhelm Wirtinger},
  journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
  volume={1905},
  pages={214 - 219}
}
  • W. Wirtinger
  • Journal für die reine und angewandte Mathematik (Crelles Journal)
Counting prime polynomials and measuring complexity and similarity of information
TLDR
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.
Some functional relations derived from the Lindelöf-Wirtinger expansion of the Lerch transcendent function
TLDR
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.
Asymptotics of Stirling and Chebyshev‐Stirling Numbers of the Second Kind
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
Euler–Frobenius numbers
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
Series Representations at Special Values of Generalized Hurwitz-Lerch Zeta Function
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
Asymptotic behavior of the Lerch transcendent function
A Necessary Condition for a Nontrivial Zero of the Riemann Zeta Function via the Polylogarithmic Function
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
On Two Applications of Herschel's Theorem
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