Series of Reciprocal Powers of k-almost Primes
arXiv:0803.0900
Abstract
Sums over inverse s-th powers of semiprimes and k-almost primes are transformed into sums over products of powers of ordinary prime zeta functions. Multinomial coefficients known from the cycle decomposition of permutation groups play the role of expansion coefficients. Founded on a known convergence acceleration for the ordinary prime zeta functions, the sums and first derivatives are tabulated with high precision for indices k=2,...,6 and integer powers s=2,...,8.
arXiv commentAdded Section 1, Equations 4+5, Remark 2, Table 2, and Section 4.3
References in corpus (5)
- Partition Identities for the Multiple Zeta Function
- Squares and Cubes Modulo n
- Twenty Digits of Some Integrals of the Prime Zeta Function
- Corrigenda to "Interesting Series Involving the Central Binomial Coefficient" [Am. Math. Monthly vol 92 (1985)]
- Time- and Space-Efficient Evaluation of Some Hypergeometric Constants
Cited by in corpus (8)
- Almost primes and the Banks-Martin conjecture
- Iterated primitives of logarithmic powers
- Table of Dirichlet L-Series and Prime Zeta Modulo Functions for Small Moduli
- Hardy-Littlewood Constants Embedded into Infinite Products over All Positive Integers
- Survey of Dirichlet Series of Multiplicative Arithmetic Functions
- Twenty Digits of Some Integrals of the Prime Zeta Function
- On the genesis of BBP formulas
- Errata and Addenda to Mathematical Constants