@article{3dc562d15ead469bad80f59f30d540f4,
title = "STRICHARTZ ESTIMATES FOR THE SCHR{\"O}DINGER EQUATION ON NON-RECTANGULAR TWO-DIMENSIONAL TORI",
abstract = "We propose a conjecture for long time Strichartz estimates on generic (non-rectangular) flat tori. We proceed to partially prove it in dimension 2. Our arguments involve on the one hand Weyl bounds; and on the other hands bounds on the number of solutions of Diophantine problems.",
author = "Yu Deng and Pierre Germain and Larry Guth and Myerson, {Simon L.Rydin}",
note = "Funding Information: Research of the first author supported by NSF grant DMS-1900251; research of the second author supported by NSF grant DMS-1501019, by the Simons collaborative grant on weak turbulence, and by the Center for Stability, Instability and Turbulence (NYUAD); research of the third author supported by a Simons Investigator Award; research of the fourth author supported by the Engineering and Physical Sciences Research Council [EP/M507970/1], by the European Research Council under ERC grant agreement no. 670239, by the Fields Institute for Research in Mathematical Sciences, and by NSF grant DMS-1363013. American Journal of Mathematics 144 (2022), 701–745. {\textcopyright} 2022 by Johns Hopkins University Press. Publisher Copyright: {\textcopyright} 2022 by Johns Hopkins University Press.",
year = "2022",
month = jun,
doi = "10.1353/ajm.2022.0014",
language = "English (US)",
volume = "144",
pages = "701--745",
journal = "American Journal of Mathematics",
issn = "0002-9327",
publisher = "Johns Hopkins University Press",
number = "3",
}