View More View Less
  • 1 ELTE, , Pázmány P. Sétány. 1/C, H-1117 Budapest, , Hungary
Open access

We give all functions ƒ , E: ℕ → ℂ which satisfy the relation

ƒ(a2+b2+c2+h) =E(a) +E(b) +E(c) +K

for every a, b, c ∈ ℕ, where h ≥ 0 is an integers and K is a complex number. If n cannot be written as a2 + b2 + c2 + h for suitable a, b, c ∈ ℕ, then ƒ (n) is not determined. This is more complicated if we assume that ƒ and E are multiplicative functions.

  • [1]

    Elliott, P. D. T. A. Probabilistic Number Theory I.. Grund. der Math. Wiss., 239, Springer-Verlag, New York, Berlin, 1979.

  • [2]

    Grosswald, E. Representations of Integers as Sums of Squares. Springer, 2011.

  • [3]

    Khanh, B. M. M. On conjecture concerning the functional equation. Annales Univ. Sci. Budapest., Sect. Comp. 46 (2017), 123135.

  • [4]

    Khanh, B. M. M. A note on a result of B. Bojan. Annales Univ. Sci. Budapest., Sect. Comp. 49 (2019), 285297.

  • [5]

    Khanh, B. M. M. On the equation f(n2+Dm2+k)=f(n)2+Df(m)2+k. Annales Univ. Sci. Budapest., Sect. Comp. 52 (2021), 217241.

  • [6]

    Park, Poo-Sung. Multiplicative function commutable with sums of squares. International Journal of Number Theory 14, 2 (2018), 469478.

    • Search Google Scholar
    • Export Citation
  • [7]

    Park, Poo-Sung. On k-additive uniqueness of the set of squares for multiplicative functions. Aequationes mathematicae 92 (2018), 487495.

    • Search Google Scholar
    • Export Citation
  • [8]

    Katái, I. and Phong, B. M. A characterization of functions using Lagrange’s Four-Square Theorem. Annales Univ. Sci. Budapest., Sect. Comp. 52 (2021), 177185.

    • Search Google Scholar
    • Export Citation
  • [9]

    Katái, I. and Phong, B. M. Arithmetical functions commutable with sums of squares. Notes on Number Theory and Discrete Mathematics 27, 3 (2021), 143154.

    • Search Google Scholar
    • Export Citation
The Instruction for Authors is available in PDF format. Please, download the file from HERE.
Please, download the LaTeX template from HERE.

Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • István GYŐRI (University of Pannonia, Veszprém)
  • János PINTZ (Rényi Institute of Mathematics)
  • Ferenc SCHIPP (Eötvös University Budapest and University of Pécs)
  • Sándor SZABÓ (University of Pécs)
     

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz)
  • Ferenc HARTUNG (University of Pannonia, Veszprém)
  • Ferenc WEISZ (Eötvös University, Budapest)

Editorial Board

  • György DÓSA (University of Pannonia, Veszprém)
  • István BERKES (Rényi Institute of Mathematics)
  • Károly BEZDEK (University of Calgary)
  • Balázs KIRÁLY – Managing Editor (University of Pécs)
  • Vedran KRCADINAC (University of Zagreb) 
  • Željka MILIN ŠIPUŠ (University of Zagreb)
  • Margit PAP (University of Pécs)
  • Mihály PITUK (University of Pannonia, Veszprém)
  • Jörg THUSWALDNER (Montanuniversität Leoben)
  • Zsolt TUZA (University of Pannonia, Veszprém)

Advisory Board

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

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

Publication Model Gold Open Access
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)