Author:
János Pintz HUN-REN Alfréd Rényi Mathematical Institute, H-1053 Budapest, Reáltanoda u. 13–15, Hungary

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We prove zero density theorems for Dedekind zeta functions in the vicinity of the line Re s = 1, improving an earlier result of W. Staś.

  • [1]

    Bourgain, J. On large values estimates for Dirichlet polynomials and the density hypothesis for the Riemann zeta function. Internat Math. Res. Notices 3 (2000), 133146.

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    Halász, G. Über die Mittelwerte multiplikativer zahlentheoretischer Funktionen. Acta Math. Hungar. 19, 3-4 (1968), 365404.

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    Halász, G. and Turán, P. On the distribution of roots of Riemann zeta and allied functions, I. J. Number Theory 1 (1969), 121137.

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    Heath-Brown, D. R. On the density of the zeros of the Dedekind Zeta-function. Acta Arith. 33 (1977), 169181.

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    Landau, E. Einführung in die elementare und analytische Theorie der algebraischen Zahlen und Ideale. Teubner, Leipzig, 1918.

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    Narkiewicz, W. Elementary and analytic theory of algebraic numbers. Monogr. Mat. 57 (Mathematical Monographs), PWN – Polish Scientific Publishers, Warsaw, 1974.

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  • [7]

    Paul, B., and Sankaranarayanan, A. On the error term and zeros of Dedekind zeta function. J. Number Theory 215 (2020), 98119.

  • [8]

    Pintz, J. Remark on a general zero density theorem. Math. Pannon 29_NS3, 2 (2023), 238243.

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    Pintz, J. Density theorems for Riemann’s zeta-function near the line Re 𝑠 = 1. Acta Arith. 208, 1 (2023), 113.

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    Pintz, J. A density theorem for Dedekind zeta functions. Math. Pannon 30_NS4, 1 (2024), 1420.

  • [11]

    Pintz, J. On a general density theorem. Acta Arith. DOI:

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    Sokolovsky, A. V. A theorem on the zeros of Dedekind’s Zeta-function and the distance between ‘neighbouring’ prime ideals (in Russian). Acta Arith. 13 (1968), 321334.

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  • [13]

    Staś, W. On the order of Dedekind zeta function near the line 𝜎 = 1. Acta Arith. 35, 2 (1979), 195202.

  • [14]

    Staś, W. An explicit estimate for zeros of Dedekind zeta functions. Acta Arith. 37 (1980), 4354.

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    Turán, P. On a new method of the analysis and its applications. (Published posthumously, with the assistance of G. Halász and J. Pintz). John Wiley & Sons, New York, 1984.

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Editor in Chief: László TÓTH, University of Pécs, Pécs, Hungary

Honorary Editors in Chief:

  • † István GYŐRI, University of Pannonia, Veszprém, Hungary
  • János PINTZ, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • Ferenc SCHIPP, Eötvös Loránd University, Budapest, Hungary and University of Pécs, Pécs, Hungary
  • Sándor SZABÓ, University of Pécs, Pécs, Hungary
     

Deputy Editors in Chief:

  • Erhard AICHINGER, JKU Linz, Linz, Austria
  • Ferenc HARTUNG, University of Pannonia, Veszprém, Hungary
  • Ferenc WEISZ, Eötvös Loránd University, Budapest, Hungary

Editorial Board

  • Attila BÉRCZES, University of Debrecen, Debrecen, Hungary
  • István BERKES, Rényi Institute of Mathematics, Budapest, Hungary
  • Károly BEZDEK, University of Calgary, Calgary, Canada
  • György DÓSA, University of Pannonia, Veszprém, Hungary
  • Balázs KIRÁLY – Managing Editor, University of Pécs, Pécs, Hungary
  • Vedran KRCADINAC, University of Zagreb, Zagreb, Croatia 
  • Željka MILIN ŠIPUŠ, University of Zagreb, Zagreb, Croatia
  • Gábor NYUL, University of Debrecen, Debrecen, Hungary
  • Margit PAP, University of Pécs, Pécs, Hungary
  • István PINK, University of Debrecen, Debrecen, Hungary
  • Mihály PITUK, University of Pannonia, Veszprém, Hungary
  • Lukas SPIEGELHOFER, Montanuniversität Leoben, Leoben, Austria
  • Andrea ŠVOB, University of Rijeka, Rijeka, Croatia
  • Csaba SZÁNTÓ, Babeş-Bolyai University, Cluj-Napoca, Romania
  • Jörg THUSWALDNER, Montanuniversität Leoben, Leoben, Austria
  • Zsolt TUZA, University of Pannonia, Veszprém, Hungary

Advisory Board

  • Szilárd RÉVÉSZ – Chair, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • Gabriella BÖHM
  • György GÁT, University of Debrecen, Debrecen, Hungary

University of Pécs,
Faculty of Sciences,
Institute of Mathematics and Informatics
Department of Mathematics
7624 Pécs, Ifjúság útja 6., HUNGARY
(36) 72-503-600 / 4179
ltoth@gamma.ttk.pte.hu

  • Mathematical Reviews
  • Zentralblatt
  • DOAJ

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Online only
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Subscription Information Gold Open Access

Mathematica Pannonica
Language English
Size A4
Year of
Foundation
1990
Volumes
per Year
1
Issues
per Year
2
Founder Akadémiai Kiadó
Founder's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)