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- W1676097218 abstract "For the positive integer $n$, let $f(n)$ denote the number of positive integer solutions $(n_1, n_2, n_3)$ of the Diophantine equation $$ {4over n}={1over n_1}+{1over n_2}+{1over n_3}. $$ For the prime number $p$, $f(p)$ can be split into $f_1(p)+f_2(p),$ where $f_i(p)(i=1, 2)$ counts those solutions with exactly $i$ of denominators $n_1, n_2, n_3$ divisible by $p.$ Recently Terence Tao proved that $$ sum_{p< x}f_1(p)ll xexp({clog xover loglog x}) $$ with other results. In this paper we shall improve it to $$ sum_{p< x}f_1(p)ll xlog^5xloglog^2x. $$" @default.
- W1676097218 created "2016-06-24" @default.
- W1676097218 creator A5031372475 @default.
- W1676097218 date "2011-07-29" @default.
- W1676097218 modified "2023-10-18" @default.
- W1676097218 title "On the estimate for a mean value relative to 4/p=1/n_1+1/n_2+1/n_3" @default.
- W1676097218 cites W121096392 @default.
- W1676097218 doi "https://doi.org/10.48550/arxiv.1107.6039" @default.
- W1676097218 hasPublicationYear "2011" @default.
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