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

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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.

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    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.

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    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).

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  • [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.

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  • [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.

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Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém, Hungary)
  • János PINTZ (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)
  • Jörg THUSWALDNER (Montanuniversität Leoben, Leoben, Austria)
  • Zsolt TUZA (University of Pannonia, Veszprém, Hungary)

Advisory Board

  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics, Budapest, Hungary)  - Chair
  • Gabriella BÖHM
  • György GÁT (University of Debrecen, Debrecen, Hungary)

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Mathematica Pannonica
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