×

zbMATH — the first resource for mathematics

Lagrange inversion theorem for Dirichlet series. (English) Zbl 07267884
Summary: We prove an analogue of the Lagrange Inversion Theorem for Dirichlet series. The proof is based on studying properties of Dirichlet convolution polynomials, which are analogues of convolution polynomials introduced by D. Knuth in [“Convolution polynomials”, Math. J. 2, 67–78 (1992)].
MSC:
30B50 Dirichlet series, exponential series and other series in one complex variable
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bayart, F., Hardy spaces of Dirichlet series and their composition operators, Monatshefte Math., 136, 203-236 (2002) · Zbl 1076.46017
[2] Burlachenko, E., The Riordan-Dirichlet group, Math. Notes, 106, 4, 514-525 (2019) · Zbl 1429.15034
[3] Choi, Y. S.; Kim, U. Y.; Maestre, M., Banach spaces of general Dirichlet series, J. Math. Anal. Appl., 465, 2, 839-856 (2018) · Zbl 1408.30001
[4] Gordon, J.; Hedenmalm, H., The composition operators on the space of Dirichlet series with square summable coefficients, Mich. Math. J., 46, 2, 313-329 (1999) · Zbl 0963.47021
[5] Knuth, D., Convolution polynomials, Math. J., 2, 67-78 (1992)
[6] Kuznetsov, A., On Dirichlet series and functional equations, J. Number Theory, 180, 498-511 (2017) · Zbl 1421.11073
[7] Scott, A. D.; Sokal, A. D., Some variants of the exponential formula, with application to the multivariate Tutte polynomial (alias Potts model), Sémin. Lothar. Comb., 61A, Article B61Ae pp. (2009) · Zbl 1283.05138
[8] Stanley, R. P., Enumerative Combinatorics, vol. 2 (1999), Cambridge University Press · Zbl 0928.05001
[9] Zeng, J., Multinomial convolution polynomials, Discrete Math., 160, 1, 219-228 (1996) · Zbl 0860.05005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.