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- W1543352053 abstract "We use bounds of mixed character sums modulo a square-free integer $q$ of a special structure to estimate the density of integer points on the hypersurface $$ f_1(x_1) + ldots + f_n(x_n) =a x_1^{k_1} ldots x_n^{k_n} $$ for some polynomials $f_i in {mathbb Z}[X]$ and nonzero integers $a$ and $k_i$, $i=1, ldots, n$. In the case of $$ f_1(X) = ldots = f_n(X) = X^2quad text{and} quad k_1 = ldots = k_n =1 $$ the above hypersurface is known as the Markoff-Hurwitz hypersurface, while for $$ f_1(X) = ldots = f_n(X) = X^nquad text{and} quad k_1 = ldots = k_n =1 $$ it is known as the Dwork hypersurface. Our results are substantially stronger than those known for general hypersurfaces." @default.
- W1543352053 created "2016-06-24" @default.
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- W1543352053 date "2014-08-19" @default.
- W1543352053 modified "2023-09-23" @default.
- W1543352053 title "On the Density of Integer Points on Generalised Markoff-Hurwitz and Dwork Hypersurfaces" @default.
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- W1543352053 doi "https://doi.org/10.48550/arxiv.1408.4514" @default.
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