000036750 001__ 36750
000036750 005__ 20210121082858.0
000036750 0247_ $$2doi$$a10.1007/s00605-015-0736-5
000036750 0248_ $$2sideral$$a90661
000036750 037__ $$aART-2015-90661
000036750 041__ $$aeng
000036750 100__ $$aAyuso, Pedro
000036750 245__ $$aA von Staudt-type result for $\displaystyle{\sum_{z\in\mathbb{Z}_n[i]} z^k }$
000036750 260__ $$c2015
000036750 5060_ $$aAccess copy available to the general public$$fUnrestricted
000036750 5203_ $$an 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….
000036750 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000036750 590__ $$a0.664$$b2015
000036750 591__ $$aMATHEMATICS$$b131 / 312 = 0.42$$c2015$$dQ2$$eT2
000036750 592__ $$a0.855$$b2015
000036750 593__ $$aMathematics (miscellaneous)$$c2015$$dQ2
000036750 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000036750 700__ $$aGrau, José María
000036750 700__ $$0(orcid)0000-0002-8191-3199$$aOller Marcén, Antonio M.
000036750 773__ $$g178, 3 (2015), 345-359$$pMon.hefte Math.$$tMONATSHEFTE FUR MATHEMATIK$$x0026-9255
000036750 8564_ $$s263082$$uhttps://zaguan.unizar.es/record/36750/files/texto_completo.pdf$$yPostprint
000036750 8564_ $$s33630$$uhttps://zaguan.unizar.es/record/36750/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000036750 909CO $$ooai:zaguan.unizar.es:36750$$particulos$$pdriver
000036750 951__ $$a2021-01-21-08:14:20
000036750 980__ $$aARTICLE