Mathematica Pannonica
Volume/Issue:
Volume 27_NS1: Issue 2
Arithmetical Functions Commutable with Sums of Squares II
Authors:
Imre Kátai ELTE, Pázmány P. Sétány. 1/C, H-1117 Budapest, Hungary

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Bui Minh Phong ELTE, Pázmány P. Sétány. 1/C, H-1117 Budapest, Hungary

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Pages:
179–190
Online Publication Date:
26 Oct 2021
Publication Date:
18 Nov 2021
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2021.00016
Keywords:
Arithmetical function; function equation; Dirichlet character; multiplicative function
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.

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    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), 217–241.

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    Park, Poo-Sung. On k-additive uniqueness of the set of squares for multiplicative functions. Aequationes mathematicae 92 (2018), 487–495.

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    Katái, I. and Phong, B. M. A characterization of functions using Lagrange’s Four-Square Theorem. Annales Univ. Sci. Budapest., Sect. Comp. 52 (2021), 177–185.

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    Katái, I. and Phong, B. M. Arithmetical functions commutable with sums of squares. Notes on Number Theory and Discrete Mathematics 27, 3 (2021), 143–154.

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Cover Mathematica Pannonica
Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752

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

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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.
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ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)

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