@article{b11066e420ce4803b147b1b9f5fe76e4,
title = "Weak Subconvexity Without A Ramanujan Hypothesis",
abstract = "We describe a new method to obtain weak subconvexity bounds for L-functions with mild hypotheses on the size of the Dirichlet coefficients. We verify these hypotheses for all automorphic L-functions and (with mild restrictions) the Rankin-Selberg Lfunctions attached to two automorphic representations. The proof relies on a new unconditional log-free zero density estimate for Rankin-Selberg L-functions.",
author = "Kannan Soundararajan and Jesse Thorner and Farrell Brumley",
note = "Funding Information: 1Brumley{\textquoteright}s work was supported by Agence Nationale de la Recherche grant 14-CE25. In addition, he would like to thank Kannan Soundararajan and Jesse Thorner for allowing him to include this Appendix to their paper, and for helpful discussions regarding the proof during a visit to Stanford. Funding Information: Acknowledgments. We thank Dimitris Koukoulopoulos, James Maynard, and Maksym Radziwi{\l}{\l} for many helpful conversations. We are particularly grateful to Paul Nelson and Dinakar Ramakrishnan for discussions regarding Lemma 2.1 including pointing out [7], and to Farrell Brumley for supplying the Appendix. Finally, we thank the anonymous referees for their helpful comments. Kannan Soundararajan was partially supported by National Science Foundation (NSF) grant DMS-1500237 and by a Simons Investigator grant from the Simons Foundation. Jesse Thorner was partially supported by an NSF Postdoctoral Fellowship. Part of this work was carried out when the authors were in residence at the Mathematical Sciences Research Institute, Berkeley, California, during the spring semester of 2017, supported in part by NSF grant DMS-1440140. Funding Information: We thank Dimitris Koukoulopoulos, James Maynard, and Maksym Radziwill for many helpful conversations. We are particularly grateful to Paul Nelson and Dinakar Ramakrishnan for discussions regarding Lemma 2.1 including pointing out [7], and to Farrell Brumley for supplying the Appendix. Finally, we thank the anonymous referees for their helpful comments. Kannan Soundararajan was partially supported by National Science Foundation (NSF) grant DMS-1500237 and by a Simons Investigator grant from the Simons Foundation. Jesse Thorner was partially supported by an NSF Postdoctoral Fellowship. Part of this work was carried out when the authors were in residence at the Mathematical Sciences Research Institute, Berkeley, California, during the spring semester of 2017, supported in part by NSF grant DMS-1440140. Publisher Copyright: {\textcopyright} 2019.",
year = "2019",
month = may,
day = "15",
doi = "10.1215/00127094-2018-0065",
language = "English (US)",
volume = "168",
pages = "1231--1268",
journal = "Duke Mathematical Journal",
issn = "0012-7094",
publisher = "Duke University Press",
number = "7",
}