Exceptional sets in Waring's problem: two squares and s biquadrates

Lilu Zhao

Lilu Zhao

Acta Arithmetica, Tome 166 (2014), p. 369-379 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $R_{s} (n)$ denote the number of representations of the positive number n as the sum of two squares and s biquadrates. When $s = 3$ or 4, it is established that the anticipated asymptotic formula for $R_{s} (n)$ holds for all $n \leq X$ with at most $O (X^{(9 - 2 s) / 8 + ε})$ exceptions.

Publié le : 2014-01-01

Zbl 1302.11078

EUDML-ID : urn:eudml:doc:279260

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     title = {Exceptional sets in Waring's problem: two squares and s biquadrates},
     journal = {Acta Arithmetica},
     volume = {166},
     year = {2014},
     pages = {369-379},
     zbl = {1302.11078},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-4-4}
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Lilu Zhao. Exceptional sets in Waring's problem: two squares and s biquadrates. Acta Arithmetica, Tome 166 (2014) pp. 369-379. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-4-4/