{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:39:59Z","timestamp":1760143199451,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,25]],"date-time":"2024-01-25T00:00:00Z","timestamp":1706140800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Let \u0393 be a non-uniform lattice in SL(2,R). In this paper, we study various L2-norms of automorphic representations of SL(2,R). We bound these norms with intrinsic norms defined on the representation. Comparison of these norms can help us understand the growth of L-functions in a systematic way.<\/jats:p>","DOI":"10.3390\/axioms13020080","type":"journal-article","created":{"date-parts":[[2024,1,25]],"date-time":"2024-01-25T08:44:07Z","timestamp":1706172247000},"page":"80","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Certain L2-Norms on Automorphic Representations of SL(2, R)"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4034-3812","authenticated-orcid":false,"given":"Hongyu","family":"He","sequence":"first","affiliation":[{"name":"Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,25]]},"reference":[{"key":"ref_1","unstructured":"Harish, C. (1968). Automorphic Forms on Semisimple Lie Groups, Springer. Notes by J. G. M. 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Math."},{"key":"ref_11","first-page":"253","article-title":"Generalized matrix coefficients for infinite dimensional unitary representations","volume":"29","author":"He","year":"2014","journal-title":"J. Ramanujan Math. Soc."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Goldfeld, D. (2006). Automorphic Forms and L-Functions for the Group GL(n,R), Cambridge University Press.","DOI":"10.1017\/CBO9780511542923"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"499","DOI":"10.2307\/2374103","article-title":"On Euler Products and the Classification of Automorphic Representations I","volume":"3","author":"Jacquet","year":"1981","journal-title":"Am. J. Math."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Borel, A. (1997). 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