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

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Bui Minh PhongELTE, 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. Multiplicative function commutable with sums of squares. International Journal of Number Theory 14, 2 (2018), 469–478.

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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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  • [9]

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

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

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

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