Waring problem with the Ramanujan $τ$-function

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dc.creatorGaraev, M. Z.
dc.creatorGarcia, V. C.
dc.creatorKonyagin, S. V.
dc.date2006-07-06
dc.date.accessioned2026-07-07T07:18:06Z
dc.date.available2026-07-07T07:18:06Z
dc.descriptionLet $τ(n)$ be the Ramanujan $τ$-function. We prove that for any integer $N$ the diophantine equation $$ \sum_{i=1}^{74000}τ(n_i)=N $$ has a solution in positive integers $n_1, n_2,..., n_{74000}$ satisfying the condition $$ \max_{1\le i\le 74000}n_i\ll |N|^{2/11}+1. $$ We also consider similar questions in the residue ring modulo a large prime $p.$
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math/0607169
dc.identifierhttp://arxiv.org/abs/math/0607169
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/114183
dc.subjectNumber Theory
dc.subject11B13, 11F35
dc.titleWaring problem with the Ramanujan $τ$-function
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