On the lower order of an entire Dirichlet series

Singh, J. P.

doi:10.1090/S0002-9939-1975-0374423-9

On the lower order of an entire Dirichlet series
HTML articles powered by AMS MathViewer

by J. P. Singh PDF

Proc. Amer. Math. Soc. 52 (1975), 209-211 Request permission

Abstract:

The lower order ${\overline \lambda _s}$ of $f(s)$ in each horizontal strip $S(\pi a)$, with $a > {\Delta ^{\ast }}$, is equal to the lower order $\lambda$ of $f(s)$. The purpose of this note is to offer a proof of this result.

References

Maurice Blambert, Sur la notion de type de l’ordre d’une fonction entière, Ann. Sci. École Norm. Sup. (3) 79 (1962), 353–375 (French). MR 0179358
Paul Malliavin, Sur quelques procédés d’extrapolation, Acta Math. 93 (1955), 179–255 (French). MR 75297, DOI 10.1007/BF02392523
S. Mandelbrojt, Dirichlet series, Rice Inst. Pamphlet 31 (1944), 159–272. MR 12163
Q. I. Rahman, On entire functions defined by a Dirichlet series, Proc. Amer. Math. Soc. 10 (1959), 213–215. MR 122968, DOI 10.1090/S0002-9939-1959-0122968-X
Q. I. Rahman, On entire functions defined by a Dirichlet series: Correction, Proc. Amer. Math. Soc. 11 (1960), 624–625. MR 122969, DOI 10.1090/S0002-9939-1960-0122969-X
Delfina Roux, Sull’ordine inferiore delle funzioni intere, Boll. Un. Mat. Ital (3) 20 (1965), 379–388 (Italian, with English summary). MR 0194605
K. N. Srivastava, On the lower order of an entire Dirichlet series, Math. Japon. 5 (1958/59), 109–112. MR 124472
F. Sunyer i Balaguer, On entire functions defined by a Dirichlet series, Proc. Amer. Math. Soc. 11 (1960), 621–623. MR 122970, DOI 10.1090/S0002-9939-1960-0122970-6