A von Staudt-type result for $\displaystyle{\sum_{z\in\mathbb{Z}_n[i]} z^k }$
Resumen: 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….
Idioma: Inglés
DOI: 10.1007/s00605-015-0736-5
Año: 2015
Publicado en: MONATSHEFTE FUR MATHEMATIK 178, 3 (2015), 345-359
ISSN: 0026-9255

Factor impacto JCR: 0.664 (2015)
Categ. JCR: MATHEMATICS rank: 131 / 312 = 0.42 (2015) - Q2 - T2
Factor impacto SCIMAGO: 0.855 - Mathematics (miscellaneous) (Q2)

Tipo y forma: Article (PostPrint)

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