@article{a3e7df3b076d481a9e02a16bc5863b12,
title = "Bounds on 2-Torsion in class groups of number fields and integral points on elliptic curves",
author = "M. Bhargava and A. Shankar and T. Taniguchi and F. Thorne and J. Tsimerman and Y. Zhao",
note = "Funding Information: Received by the editors March 12, 2017, and, in revised form, November 1, 2019, and November 20, 2019. 2010 Mathematics Subject Classification. Primary 11G05, 11R29. The first author was supported in part by a Simons Investigator Grant and NSF Grant DMS-1001828. The third author was supported in part by the JSPS and KAKENHI Grants JP24654005 and JP25707002. The fourth author was supported in part by NSF Grant DMS-1201330, by the National Security Agency under a Young Investigator Grant, and by the Simons Foundation under Grants No. 563234 and 586594. Funding Information: The first author was supported in part by a Simons Investigator Grant and NSF Grant DMS-1001828. The third author was supported in part by the JSPS and KAKENHI Grants JP24654005 and JP25707002. The fourth author was supported in part by NSF Grant DMS-1201330, by the National Security Agency under a Young Investigator Grant, and by the Simons Foundation under Grants No. 563234 and 586594.This paper is the result of our collaboration at a SQuaRE (Structured Quartet Research Ensemble) held at the American Institute of Mathematics. We would all like to thank AIM for their financial support and for providing an excellent environment in which to work. We would like to thank Bob Hough and Pierre Le Boudec for helpful conversa-tions. We also would like to thank anonymous referees for their careful readings and many useful comments. Part of this work was done during the sixth author{\textquoteright}s stay at the Max Planck Institute for Mathematics. He is very grateful for the Institute{\textquoteright}s hospitality.",
year = "2020",
month = oct,
doi = "10.1090/jams/945",
language = "English (US)",
volume = "33",
pages = "1087--1099",
journal = "Journal of the American Mathematical Society",
issn = "0894-0347",
publisher = "American Mathematical Society",
number = "4",
}