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

Search for other papers by János Pintz in
Current site
Google Scholar
PubMed
Close
Open access

We apply a recent general zero density theorem of us (valid for a large class of complex functions) to improve earlier density theorems of Heath-Brown and Paul–Sankaranarayanan for Dedekind zeta functions attached to a number field 𝐾 of degree 𝑛 with 𝑛 > 2.

  • [1]

    Bourgain, J. Decoupling, exponential sums and the Riemann zeta function, J. Amer. Math. Soc. 30, 1 (2017), 205224.

  • [2]

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

  • [3]

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

  • [4]

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

  • [5]

    Heath-Brown, D. R. The growth rate of the Dedekind zeta-function on the critical line, Acta Arith. 49, (1988), 323339.

  • [6]

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

  • [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 /NS 3/ 2, (2023), 238243.

  • [9]

    Pintz, J. On a general density theorem. Acta Arith., to appear.

  • [10]

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

    • Search Google Scholar
    • Export Citation
  • [11]

    Titchmarsh, E. C. The theory of the Riemann zeta-function, Oxford, Clarendon Press, 1951.

  • [12]

    Turán, P. On the zeros of Riemann’s zeta-function, Collected Papers of Paul Turán, Ed. P. Erdős, Vol. 1, pp. 748759, Akadémiai Kiadó, Budapest, 1954.

    • Search Google Scholar
    • Export Citation
  • [13]

    Turán, P. On a new method of analysis and its applications. Pure and Applied Mathematics (New York). A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1984. xvi+584 pp. With the assistance of G. Halász and J. Pintz. With a foreword by Vera T. Sós.

    • Search Google Scholar
    • Export Citation
  • Collapse
  • Expand

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

Honorary Editors in Chief:

  • 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

Publication Model Gold Open Access
Online only
Submission Fee none
Article Processing Charge 0 EUR/article (temporarily)
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)