Integral Functions with Gap Power Series

P. Erdös; A. J. Macintyee

doi:10.1017/S0013091500021416

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

1. Let

be an integral function, λn being a strictly increasing sequence of nonnegative integers. We shall use the notations

describing M (r) as the maximum modulus, m (r) as the minimum modulus and μ(r) as the maximum term of f (z).

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Singh, Shri Krishna 1961. On exceptional values of entire and meromorphic functions. Tohoku Mathematical Journal, Vol. 13, Issue. 3,

Kahane, J.-P. 1964. Lacunary Taylor and Fourier series. Bulletin of the American Mathematical Society, Vol. 70, Issue. 2, p. 199.

Gray, Alfred and Shah, S. M. 1964. A note on entire functions and a conjecture of Erdös (II). Journal d'Analyse Mathématique, Vol. 12, Issue. 1, p. 83.

Gray, Alfred and Shah, S. M. 1965. Holomorphic functions with gap power series. Mathematische Zeitschrift, Vol. 86, Issue. 5, p. 375.

Shah, S. M. and Silverman, Herb 1976. Entire functions with maximum deficiency sum and their means. Mathematische Annalen, Vol. 220, Issue. 2, p. 185.

Gross, Fred 1977. Complex Analysis. Vol. 599, Issue. , p. 51.

Fenton, P. C. 1978. The minimum modulus of gap power series. Proceedings of the Edinburgh Mathematical Society, Vol. 21, Issue. 1, p. 49.

Skaskiv, O. B. 1994. On the minimum of the absolute value of the sum for a Dirichlet series with bounded sequence of exponents. Mathematical Notes, Vol. 56, Issue. 5, p. 1177.

Shang, Lina and Gao, Zongsheng 2008. Entire functions defined by Dirichlet series. Journal of Mathematical Analysis and Applications, Vol. 339, Issue. 2, p. 853.

Lina, Shang and Zongsheng, Gao 2009. The pits property of entire functions defined by Dirichlet series. Acta Mathematica Scientia, Vol. 29, Issue. 1, p. 83.

Berteloot, François and Cheraghi, Davoud 2023. Lacunary series, resonances, and automorphisms of C2 with a round Siegel domain. Kyoto Journal of Mathematics, Vol. 63, Issue. 2,

Article contents

Integral Functions with Gap Power Series

Extract

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests