Zeros and poles of Dirichlet series
Enrico Bombieri; Alberto Perelli
- Volume: 12, Issue: 2, page 69-73
- ISSN: 1120-6330
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topBombieri, 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
top- Besicovitch, A.S., Almost Periodic Functions. Cambridge University Press1954. Zbl0004.25303JFM58.0264.02
- Bombieri, E. - Perelli, A., Distinct zeros of -functions. Acta Arith., 83, 1998, 271-281. Zbl0891.11044MR1611193
- 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
- Hayman, W.K., Meromorphic Functions. Oxford University Press, 1964. Zbl0115.06203MR164038
- Levin, B. Ja., Distribution of Zeros of Entire Functions. Math. Monograph Transl., 5, Amer. Math. Soc., Providence, RI1964. Zbl0152.06703MR156975
- 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
- Raghunathan, R., A comparison of zeros of -functions. Math. Res. Letters, 6, 1999, 155-167. Zbl0978.11045MR1689206
- 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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