Research Article
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Year 1973, Volume: 22 , 0 - 0, 01.01.1973
https://doi.org/10.1501/Commua1_0000000636

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  • Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi

On The Mean Values of an Entire Function Represented By a Dirichlet Series II

Year 1973, Volume: 22 , 0 - 0, 01.01.1973
https://doi.org/10.1501/Commua1_0000000636

Abstract

In this note we prove a theorem which gives us Information as to how the functions log I§ (a) and log (a) grow relative to each other as a ^00.
Theorem. Let f(s) be an entire function represented by a Dirichlet series, then
lim
a ^00
log Ig (<’) log J8,k (o) X ■! (1 + k/X) (X 0)
(X = 0)
where X = lim
CT-^OO
log log Ig (a)
a
1. In the usual notation,
00
f(s) = s 1
Sn e®^-”, (s = (j it), 0 A, (n 1)
lim n -*oo
00
is an entire function in the sense that the Dirichlet series represen- ting it, is ahsolutely convergent for ali finite s and possesses
where 0
lim
(7-4-00
log log M(g)
(7
X, 00, and M(ct) have their usual meanings.

References

  • Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi
There are 1 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Jodh Pal Sıngh This is me

Publication Date January 1, 1973
Submission Date January 1, 1973
Published in Issue Year 1973 Volume: 22

Cite

APA Sıngh, J. P. (1973). On The Mean Values of an Entire Function Represented By a Dirichlet Series II. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 22. https://doi.org/10.1501/Commua1_0000000636
AMA Sıngh JP. On The Mean Values of an Entire Function Represented By a Dirichlet Series II. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. January 1973;22. doi:10.1501/Commua1_0000000636
Chicago Sıngh, Jodh Pal. “On The Mean Values of an Entire Function Represented By a Dirichlet Series II”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 22, January (January 1973). https://doi.org/10.1501/Commua1_0000000636.
EndNote Sıngh JP (January 1, 1973) On The Mean Values of an Entire Function Represented By a Dirichlet Series II. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 22
IEEE J. P. Sıngh, “On The Mean Values of an Entire Function Represented By a Dirichlet Series II”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 22, 1973, doi: 10.1501/Commua1_0000000636.
ISNAD Sıngh, Jodh Pal. “On The Mean Values of an Entire Function Represented By a Dirichlet Series II”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 22 (January 1973). https://doi.org/10.1501/Commua1_0000000636.
JAMA Sıngh JP. On The Mean Values of an Entire Function Represented By a Dirichlet Series II. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 1973;22. doi:10.1501/Commua1_0000000636.
MLA Sıngh, Jodh Pal. “On The Mean Values of an Entire Function Represented By a Dirichlet Series II”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 22, 1973, doi:10.1501/Commua1_0000000636.
Vancouver Sıngh JP. On The Mean Values of an Entire Function Represented By a Dirichlet Series II. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 1973;22.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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