@article { ,
title = {An asymptotic formula for integer points on Markoff-Hurwitz varieties},
abstract = {We establish an asymptotic formula for the number of integer solutions to the Markoff-Hurwitz equation x21+x22+⋯+x2n=ax1x2⋯xn+k. When n≥4, the previous best result is by Baragar (1998) that gives an exponential rate of growth with exponent β that is not in general an integer when n≥4. We give a new interpretation of this exponent of growth in terms of the unique parameter for which there exists a certain conformal measure on projective space.},
doi = {10.4007/annals.2019.190.3.2},
eissn = {1939-8980},
issn = {0003-486X},
issue = {3},
journal = {Annals of Mathematics},
note = {EPrint Processing Status: Full text deposited in DRO},
pages = {751-809},
publicationstatus = {Published},
publisher = {Department of Mathematics},
volume = {190},
year = {2019},
author = {Gamburd, Alex and Magee, Michael and Ronan, Ryan}
}