The growth of a class of random Dirichlet series on the horizontal zone

Zhendong Gu; Daochun Sun

Mathematica Bohemica (2012)

  • Volume: 137, Issue: 1, page 65-77
  • ISSN: 0862-7959

Abstract

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In the paper we obtain that, under some condition, the Rademacher-Dirichlet series or the Steinhaus-Dirichlet series on the whole plane and on the horizontal zone almost surely have the same growth.

How to cite

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Gu, Zhendong, and Sun, Daochun. "The growth of a class of random Dirichlet series on the horizontal zone." Mathematica Bohemica 137.1 (2012): 65-77. <http://eudml.org/doc/246273>.

@article{Gu2012,
abstract = {In the paper we obtain that, under some condition, the Rademacher-Dirichlet series or the Steinhaus-Dirichlet series on the whole plane and on the horizontal zone almost surely have the same growth.},
author = {Gu, Zhendong, Sun, Daochun},
journal = {Mathematica Bohemica},
keywords = {random Dirichlet series; Rademacher-Dirichlet series; Steinhaus-Dirichlet series; growth; random Dirichlet series; Rademacher-Dirichlet series; Steinhaus-Dirichlet series},
language = {eng},
number = {1},
pages = {65-77},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The growth of a class of random Dirichlet series on the horizontal zone},
url = {http://eudml.org/doc/246273},
volume = {137},
year = {2012},
}

TY - JOUR
AU - Gu, Zhendong
AU - Sun, Daochun
TI - The growth of a class of random Dirichlet series on the horizontal zone
JO - Mathematica Bohemica
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 137
IS - 1
SP - 65
EP - 77
AB - In the paper we obtain that, under some condition, the Rademacher-Dirichlet series or the Steinhaus-Dirichlet series on the whole plane and on the horizontal zone almost surely have the same growth.
LA - eng
KW - random Dirichlet series; Rademacher-Dirichlet series; Steinhaus-Dirichlet series; growth; random Dirichlet series; Rademacher-Dirichlet series; Steinhaus-Dirichlet series
UR - http://eudml.org/doc/246273
ER -

References

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  1. Kawata, T., Fourier Analysis in Probability Theory, New York, Acad. Press (1972). (1972) Zbl0271.60022MR0464353
  2. Reac, Paley, Zygmund, A., 10.1017/S0305004100016078, Proc. Camb. Phil. Soc. 26 (1930) 337-357, 458-474; 28 (1932), 190-205. DOI10.1017/S0305004100016078
  3. Bohr, H., Collected Mathematical Works, Dansk Matematisk Forening Copenhagen (1952). (1952) Zbl0049.00105MR0057790
  4. Jiarong, Yu, Some properties of random Dirichlet series, Acta Math. Sin. 21 (1978), 97-118 Chinese. (1978) MR0507192
  5. Knopp, K., Über de Konvergenzabscisse des Laplace-Integrals, Math. Z. (1951), 54 291-296 German. (1951) MR0042539
  6. Valiron, G., 10.24033/bsmf.1051, Bulletin de la Société Mathématique de France 52 (1924), 166-174 French. (1924) MR1504844DOI10.24033/bsmf.1051
  7. Tanaka, C., Note on Dirichlet series (V), On the integral functions defined by Dirichlet series (I), Tôhoku Math. J., II. Ser. (1953), 5 67-78. (1953) Zbl0053.37502MR0057320
  8. Valiron, G., Théorie genérale des séries de Dirichlet, Mémorial des sciences mathématiques, Fasc. 17 (1926), French. (1926) 
  9. Valiron, G., Entire functions and Borel's directions, Proc. Nat. Acad. Sci. USA (1934), 20 211-215. (1934) Zbl0009.02503

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