Counting prime polynomials and measuring complexity and similarity of information
- Mathematics, Computer Science
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
- MathematicsMath. Comput.
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…
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
- MathematicsJ. Approx. Theory
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…