Waring problem with the Ramanujan $τ$-function

Details Waring problem with the Ramanujan $τ$-function Waring problem with the Ramanujan $τ$-function

2006-07-06

arxiv.org/abs/math/0607169v1

Mathematics

Number Theory

17 pages

Scientific paper

Let $\tau(n)$ be the Ramanujan $\tau$-function. We prove that for any integer
$N$ the diophantine equation $$ \sum_{i=1}^{74000}\tau(n_i)=N $$ 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 $p.$

Affiliated with

Also associated with

No associations

Rating

Waring problem with the Ramanujan $τ$-function does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Waring problem with the Ramanujan $τ$-function, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Waring problem with the Ramanujan $τ$-function will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-45568