Functiones et Approximatio Commentarii Mathematici

Set of uniqueness of shifted Gaussian primes

Jay Mehta and G.K. Viswanadham

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In this paper, we show that any additive complex valued function over non-zero Gaussian integers which vanishes on the shifted Gaussian primes is necessarily identically zero.

Article information

Funct. Approx. Comment. Math., Volume 53, Number 1 (2015), 123-133.

First available in Project Euclid: 28 September 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11N36: Applications of sieve methods
Secondary: 11N64: Other results on the distribution of values or the characterization of arithmetic functions

additive functions shifted Gaussian primes set of uniqueness


Mehta, Jay; Viswanadham, G.K. Set of uniqueness of shifted Gaussian primes. Funct. Approx. Comment. Math. 53 (2015), no. 1, 123--133. doi:10.7169/facm/2015.53.1.7.

Export citation


  • P.D.T.A. Elliott, A conjecture of Kátai, Acta Arith. 26 (1974), 11–20.
  • P.D.T.A. Elliott, On two conjectures of Kátai, Acta Arith. 30 (1976), no. 4, 341–365.
  • P.D.T.A. Elliott, Arithmetic Functions and Integer Products, Springer-Verlag, New York, 1985.
  • P.D.T.A. Elliott, C. Ryavec, The distribution of the values of additive arithmetical functions, Acta Math. 126 (1971), 143–164.
  • P. Erdös, On the distribution function of additive functions, Ann. of Math. 47 (1946), 1–20.
  • H. Halberstam, H.E. Richert, Sieve Methods, London Mathematical Society Monographs, No. 4, Academic Press (London, 1974).
  • A. Hildebrand, Additive and multiplicative functions on shifted primes, Proc. London Math. Soc. (3) 59 (1989), 209–232.
  • J. Hinz, M. Lodemann, On Siegel zeros of Hecke-Landau zeta-functions, Mh. Math. 118 (1994), 231–248.
  • D. Johnson, Mean values of Hecke L-functions, J. Reine Angew. Math. 305 (1979), 195–205.
  • I. Kátai, On sets characterizing number theoretical functions, Acta Arith. 13 (1968), 315–320.
  • I. Kátai, On sets characterizing number theoretical functions-II, Acta Arith. 16 (1968), 1–4.
  • J. Mehta, G.K. Viswanadham, Quasi-uniqueness of the set of “Gaussian prime plus one's”, Int. J. Number Theory 10 (2014), no. 7, 1783–1790.
  • G.J. Rieger, Verallgemeinerung der Siebmethode von A. Selberg auf algebraische Zahlkörper I, J. Reine Angew. Math. 199 (1958), 208–214.
  • G.K. Viswanadham, Topics in Analytic number theory, Ph.D. Thesis, HBNI, March 2015.
  • E. Wirsing, Additive functions with restricted growth on the numbers of the form $p+1$, Acta Arith. 37 (1980), 345–357.
  • D. Wolke, Bemerkungen über Eindeutigkeitsmengen additiver Funcktionen, Elem. Math. 33 (1978), 14–16.