{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T04:47:07Z","timestamp":1776314827500,"version":"3.50.1"},"reference-count":28,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["546235"],"award-info":[{"award-number":["546235"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Data. Sc. Math. Sc."],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:p>In recent work with Bober, Booker, Lee, Seymour-Howell, and Zubrilina, we proved murmuration behavior for Maass forms in the eigenvalue aspect and for modular forms in the weight aspect. Both used an approach based on the Selberg trace formula. But different trace formulas, including those due to Kuznetsov or Petersson, offer different variations. We examine murmurations from the perspective of different trace formulas and outline several families of [Formula: see text]-functions where one can likely prove additional murmuration behavior.<\/jats:p>","DOI":"10.1142\/s2810939225400039","type":"journal-article","created":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T02:33:41Z","timestamp":1760063621000},"page":"63-73","source":"Crossref","is-referenced-by-count":0,"title":["On murmurations and trace formulas"],"prefix":"10.1142","volume":"03","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8543-4558","authenticated-orcid":false,"given":"David","family":"Lowry-Duda","sequence":"first","affiliation":[{"name":"Institute of Computational and Experimental Research in Mathematics, 121 South Main Street, Box E, Providence, RI 02903, USA"}]}],"member":"219","published-online":{"date-parts":[[2025,12,9]]},"reference":[{"key":"S2810939225400039BIB001","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.2024.2382361"},{"key":"S2810939225400039BIB002","doi-asserted-by":"publisher","DOI":"10.1090\/coll\/053"},{"key":"S2810939225400039BIB003","author":"Sutherland A.","year":"2024","journal-title":"Talk at Simons Center for Geometry and Physics"},{"key":"S2810939225400039BIB004","unstructured":"P. Sarnak, Letter to Drew Sutherland and Nina Zubrilina on murmurations and root numbers (2023), https:\/\/publications.ias.edu\/sarnak\/."},{"key":"S2810939225400039BIB005","unstructured":"J. Bober, A. R. Booker, M. Lee and D. Lowry-Duda, Murmurations of modular forms in the weight aspect, to appear in\n                      Algebra and Number Theory\n                      (2025), https:\/\/arxiv.org\/abs\/2310.07746."},{"key":"S2810939225400039BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/BF02698741"},{"key":"S2810939225400039BIB007","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-99-00766-1"},{"key":"S2810939225400039BIB008","volume-title":"Random Matrices, Frobenius Eigenvalues, and Monodromy","volume":"45","author":"Katz N. M.","year":"1999"},{"key":"S2810939225400039BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/BF02547776"},{"key":"S2810939225400039BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s40993-021-00302-9"},{"key":"S2810939225400039BIB011","doi-asserted-by":"publisher","DOI":"10.1093\/imrn\/rnae277"},{"key":"S2810939225400039BIB012","unstructured":"N. Zubrilina, Murmurations, preprint (2023), http:\/\/arxiv.org\/abs\/2310.07681v1."},{"key":"S2810939225400039BIB013","first-page":"403","volume":"13","author":"Yamauchi M.","year":"1973","journal-title":"J. Math. Kyoto Univ."},{"key":"S2810939225400039BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/BF01394347"},{"key":"S2810939225400039BIB015","unstructured":"Z. Wang, Murmurations of Hecke L-functions of imaginary quadratic fields, preprint (2025), http:\/\/arxiv.org\/abs\/2503.17967v1."},{"issue":"9","key":"S2810939225400039BIB016","first-page":"3721","volume":"151","author":"Martin K.","year":"2023","journal-title":"Proc. Amer. Math. Soc."},{"key":"S2810939225400039BIB017","unstructured":"K. Martin, Variations on murmurations, preprint (2025), http:\/\/arxiv.org\/abs\/2505.01093v1."},{"key":"S2810939225400039BIB018","unstructured":"A. R. Booker, M. Lee, D. Lowry-Duda, A. Seymour-Howell and N. Zubrilina, Murmurations of Maass forms, preprint (2024), arXiv:2409.00765."},{"key":"S2810939225400039BIB019","unstructured":"A. Str\u00f6mbergsson, Explicit trace formula for Hecke operators, (2016)."},{"key":"S2810939225400039BIB020","doi-asserted-by":"crossref","unstructured":"A. Seymour-Howell, Rigorous computation of maass cusp forms, PhD thesis, University of Bristol (2023).","DOI":"10.1007\/s40993-022-00393-y"},{"key":"S2810939225400039BIB021","unstructured":"A. Cowan, Murmurations and ratios conjectures, preprint (2024), http:\/\/arxiv.org\/abs\/2408.12723v3."},{"key":"S2810939225400039BIB022","doi-asserted-by":"publisher","DOI":"10.4310\/CNTP.2008.v2.n3.a4"},{"key":"S2810939225400039BIB023","unstructured":"W. Sawin and A. V. Sutherland, Murmurations for elliptic curves ordered by height, preprint (2025), http:\/\/arxiv.org\/abs\/2504.12295v1."},{"key":"S2810939225400039BIB024","doi-asserted-by":"publisher","DOI":"10.1007\/s002220200223"},{"key":"S2810939225400039BIB025","doi-asserted-by":"publisher","DOI":"10.2307\/1970831"},{"key":"S2810939225400039BIB026","unstructured":"C. I. Kuan, D. Lowry-Duda, A. Walker and R. S. Steiner, Sums of cusp form coefficients along quadratic sequences (2023) arXiv:2301.11901."},{"key":"S2810939225400039BIB027","unstructured":"D. Lowry-Duda, Murmurations in Maass forms, Talk at ICERM\n                      Murmurations in Arithmetic\n                      Workshop, 2023, https:\/\/davidlowryduda.com\/maass-murmurations\/."},{"key":"S2810939225400039BIB028","author":"Lowry-Duda D.","year":"2024","journal-title":"Talk at SCGP Murmurations in Arithmetic Geometry and Related Topics workshop"}],"container-title":["International Journal of Data Science in the Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S2810939225400039","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T03:58:29Z","timestamp":1776311909000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S2810939225400039"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12]]},"references-count":28,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["10.1142\/S2810939225400039"],"URL":"https:\/\/doi.org\/10.1142\/s2810939225400039","relation":{},"ISSN":["2810-9392","2810-9406"],"issn-type":[{"value":"2810-9392","type":"print"},{"value":"2810-9406","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12]]}}}