36750 20210121082858.0 doi 10.1007/s00605-015-0736-5 sideral 90661 ART-2015-90661 eng Ayuso, Pedro A von Staudt-type result for $\displaystyle{\sum_{z\in\mathbb{Z}_n[i]} z^k }$ 2015 Access copy available to the general public Unrestricted n this paper we study the sum of powers of the Gaussian integers Gk(n):=¿a,b¿[1,n](a+bi)k. We give an explicit formula for Gk(n)(modn) in terms of the prime numbers p=3(mod4) with p||n and p-1|k, similar to the well known one due to von Staudt for ¿ni=1ik(modn). We apply this result to study the set of integers n which divide Gn(n) and compute its asymptotic density with six exact digits: 0.971000…. info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 0.664 2015 MATHEMATICS 131 / 312 = 0.42 2015 Q2 T2 0.855 2015 Mathematics (miscellaneous) 2015 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Grau, José María (orcid)0000-0002-8191-3199 Oller Marcén, Antonio M. 178, 3 (2015), 345-359 Mon.hefte Math. MONATSHEFTE FUR MATHEMATIK 0026-9255 263082 http://zaguan.unizar.es/record/36750/files/texto_completo.pdf Postprint 33630 http://zaguan.unizar.es/record/36750/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:36750 articulos driver 2021-01-21-08:14:20 ARTICLE