Zeros and poles of Dirichlet series

Enrico Bombieri; Alberto Perelli

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2001)

  • Volume: 12, Issue: 2, page 69-73
  • ISSN: 1120-6330

Abstract

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Under certain mild analytic assumptions one obtains a lower bound, essentially of order r , for the number of zeros and poles of a Dirichlet series in a disk of radius r . A more precise result is also obtained under more restrictive assumptions but still applying to a large class of Dirichlet series.

How to cite

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Bombieri, Enrico, and Perelli, Alberto. "Zeros and poles of Dirichlet series." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 12.2 (2001): 69-73. <http://eudml.org/doc/252352>.

@article{Bombieri2001,
abstract = {Under certain mild analytic assumptions one obtains a lower bound, essentially of order $r$, for the number of zeros and poles of a Dirichlet series in a disk of radius $r$. A more precise result is also obtained under more restrictive assumptions but still applying to a large class of Dirichlet series.},
author = {Bombieri, Enrico, Perelli, Alberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {General Dirichlet series; Almost-periodic functions; Nevanlinna theory; general Dirichlet series; almost-periodic functions; uniformly almost periodic},
language = {eng},
month = {6},
number = {2},
pages = {69-73},
publisher = {Accademia Nazionale dei Lincei},
title = {Zeros and poles of Dirichlet series},
url = {http://eudml.org/doc/252352},
volume = {12},
year = {2001},
}

TY - JOUR
AU - Bombieri, Enrico
AU - Perelli, Alberto
TI - Zeros and poles of Dirichlet series
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2001/6//
PB - Accademia Nazionale dei Lincei
VL - 12
IS - 2
SP - 69
EP - 73
AB - Under certain mild analytic assumptions one obtains a lower bound, essentially of order $r$, for the number of zeros and poles of a Dirichlet series in a disk of radius $r$. A more precise result is also obtained under more restrictive assumptions but still applying to a large class of Dirichlet series.
LA - eng
KW - General Dirichlet series; Almost-periodic functions; Nevanlinna theory; general Dirichlet series; almost-periodic functions; uniformly almost periodic
UR - http://eudml.org/doc/252352
ER -

References

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  1. Besicovitch, A.S., Almost Periodic Functions. Cambridge University Press1954. Zbl0004.25303JFM58.0264.02
  2. Bombieri, E. - Perelli, A., Distinct zeros of L -functions. Acta Arith., 83, 1998, 271-281. Zbl0891.11044MR1611193
  3. Davenport, H. - Heilbronn, H., On the zeros of certain Dirichlet series (second paper). J. London Math. Soc., 11, 1936, 181-185; Collected Works, vol. IV, Academic Press, 1977, 1774-1779. Zbl0014.21601MR1574345JFM62.0138.01
  4. Hayman, W.K., Meromorphic Functions. Oxford University Press, 1964. Zbl0115.06203MR164038
  5. Levin, B. Ja., Distribution of Zeros of Entire Functions. Math. Monograph Transl., 5, Amer. Math. Soc., Providence, RI1964. Zbl0152.06703MR156975
  6. Murty, M. R. - Murty, V. K., Strong multiplicity one for Selberg’s class. C. R. Acad. Sci. Paris Sér. I Math., 319, 1994, 315-320. Zbl0823.11049MR1289304
  7. Raghunathan, R., A comparison of zeros of L -functions. Math. Res. Letters, 6, 1999, 155-167. Zbl0978.11045MR1689206
  8. Selberg, A., Old and new conjectures and results about a class of Dirichlet series. In: E. Bombieri et al. (eds.), Proc. Amalfi Conf. Analytic Number Theory, Università di Salerno 1992, 367-385; Collected Papers, vol. II, Springer-Verlag, 1991, 47-63. Zbl0787.11037MR1220477

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