An asymptotic formula for integer points on Markoff-Hurwitz varieties

Published: 19/07/2019
An asymptotic formula for integer points on Markoff-Hurwitz varieties
Source: MATH.PRINCETON.EDU

We establish an asymptotic formula for the number of integer solutions to the Markoff-Hurwitz equation \[ x_{1}^{2}+x_{2}^{2}+\ldots+x_{n}^{2}=ax_{1}x_{2}\ldots x_{n}+k. \] When $n\geq4$ the previous best result is by Baragar (1998) that gives an exponential rate of growth with exponent $\beta$ that … Continue reading →

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