{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T14:33:26Z","timestamp":1763390006561,"version":"3.45.0"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T00:00:00Z","timestamp":1753142400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T00:00:00Z","timestamp":1753142400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1007\/s10998-025-00666-w","type":"journal-article","created":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T07:43:51Z","timestamp":1753170231000},"page":"479-493","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the second moment of the Fourier coefficients of symmetric power L-function over two sparse sequences of positive integers"],"prefix":"10.1007","volume":"91","author":[{"given":"Jinzhi","family":"Feng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,7,22]]},"reference":[{"key":"666_CR1","doi-asserted-by":"crossref","unstructured":"P. Deligne. La conjecture de Weil. I. Inst. Hautes \u00c9tudes Sci. Publ. Math., 43:273\u2013307, 1974","DOI":"10.1007\/BF02684373"},{"issue":"5","key":"666_CR2","first-page":"246","volume":"19","author":"OM Fomenko","year":"2007","unstructured":"O.M. Fomenko, Mean value theorems for automorphic $$L$$-functions. Algebra i Analiz 19(5), 246\u2013264 (2007)","journal-title":"Algebra i Analiz"},{"key":"666_CR3","doi-asserted-by":"crossref","unstructured":"S.W.Graham ,G.Kolesnik, Van der Corput\u2019s method of exponential sums, vol. 126 (Cambridge University Press, Cambridge, 1991)","DOI":"10.1017\/CBO9780511661976"},{"key":"666_CR4","unstructured":"G.H. Hardy, E.M. Wright, An introduction to the theory of numbers (Oxford University Press, Oxford, fifth edition, 1979)"},{"issue":"7","key":"666_CR5","doi-asserted-by":"publisher","first-page":"2847","DOI":"10.1090\/proc\/14516","volume":"147","author":"X He","year":"2019","unstructured":"X. He, Integral power sums of Fourier coefficients of symmetric square $$L$$-functions. Proc. Amer. Math. Soc. 147(7), 2847\u20132856 (2019)","journal-title":"Proc. Amer. Math. Soc."},{"key":"666_CR6","doi-asserted-by":"crossref","unstructured":"D.R. Heath-Brown. A new $$k$$th derivative estimate for a trigonometric sum via Vinogradov\u2019s integral. Tr. Mat. Inst. Steklova, 296:95\u2013110, 2017. English version published in Proc. Steklov Inst. Math. 296(1). (2017), 88\u2013103","DOI":"10.1134\/S0081543817010072"},{"key":"666_CR7","doi-asserted-by":"crossref","unstructured":"G.Hua. The average behaviour of Hecke eigenvalues over certain sparse sequence of positive integers. Res. Number Theory, 8(4):Paper No. 95, 20, 2022","DOI":"10.1007\/s40993-022-00403-z"},{"key":"666_CR8","doi-asserted-by":"crossref","unstructured":"A.Ivi\u0107 ,W.Zhai. On a hybrid fourth moment involving the Riemann zeta-function. In Topics in mathematical analysis and applications, volume\u00a094 of Springer Optim. Appl., pages 461\u2013482. Springer, Cham, Switzerland, 2014","DOI":"10.1007\/978-3-319-06554-0_19"},{"key":"666_CR9","doi-asserted-by":"crossref","unstructured":"H. Iwaniec, E. Kowalski, Analytic number theory, American Mathematical Society Colloquium Publications, vol. 53. (American Mathematical Society, Providence, RI, 2004)","DOI":"10.1090\/coll\/053"},{"issue":"13","key":"666_CR10","doi-asserted-by":"publisher","first-page":"11453","DOI":"10.1093\/imrn\/rnac153","volume":"2023","author":"Y Lin","year":"2023","unstructured":"Y. Lin, R. Nunes, Z. Qi, Strong subconvexity for self-dual $$\\rm GL(3)$$$$L$$-functions. Int. Math. Res. Not. IMRN 2023(13), 11453\u201311470 (2023)","journal-title":"Int. Math. Res. Not. IMRN"},{"key":"666_CR11","doi-asserted-by":"crossref","unstructured":"H.Liu. The average behavior of Fourier coefficients of symmetric power $$L$$-functions. Bull. Malays. Math. Sci. Soc., 46(6):Paper No. 193, 15, 2023","DOI":"10.1007\/s40840-023-01586-z"},{"key":"666_CR12","doi-asserted-by":"crossref","unstructured":"H. Liu ,X. Yang. The average behaviors of the Fourier coefficients of $$j$$-th symmetric power $$L$$-function over two sparse sequences of positive integers. Bull. Iranian Math. Soc., 50(1):Paper No. 14, 16, 2024","DOI":"10.1007\/s41980-023-00850-z"},{"issue":"3","key":"666_CR13","first-page":"253","volume":"199","author":"S Luo","year":"2021","unstructured":"S. Luo, H. Lao, A. Zou, Asymptotics for the Dirichlet coefficients of symmetric power $$L$$-functions. Acta Arith 199(3), 253\u2013268 (2021)","journal-title":"Acta Arith"},{"key":"666_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10240-021-00127-3","volume":"134","author":"J Newton","year":"2021","unstructured":"J. Newton, J.A. Thorne, Symmetric power functoriality for holomorphic modular forms. Publ. Math. Inst. Hautes \u00c9tudes Sci. 134, 1\u2013116 (2021)","journal-title":"Publ. Math. Inst. Hautes \u00c9tudes Sci."},{"key":"666_CR15","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1007\/BF01761499","volume":"130","author":"A Perelli","year":"1982","unstructured":"A. Perelli, General $$L$$-functions. Ann. Mat. Pura Appl. 130, 287\u2013306 (1982)","journal-title":"Ann. Mat. Pura Appl."},{"issue":"2","key":"666_CR16","doi-asserted-by":"publisher","first-page":"193","DOI":"10.4064\/aa180819-6-10","volume":"190","author":"A Sankaranarayanan","year":"2019","unstructured":"A. Sankaranarayanan, S.K. Singh, K. Srinivas, Discrete mean square estimates for coefficients of symmetric power $$L$$-functions. Acta Arith 190(2), 193\u2013208 (2019)","journal-title":"Acta Arith"},{"key":"666_CR17","unstructured":"A. Sharma,A. Sankaranarayanan. Average behavior of the Fourier coefficients of the symmetric square $$L$$-function over some sequence of integers. Integers, 22:Paper No. A74, 17, 2022"},{"key":"666_CR18","doi-asserted-by":"crossref","unstructured":"A. Sharma,A. Sankaranarayanan. Discrete mean square of the coefficients of symmetric square $$L$$-functions on certain sequence of positive numbers. Res. Number Theory, 8(1):Paper No. 19, 13, 2022","DOI":"10.1007\/s40993-022-00319-8"},{"key":"666_CR19","doi-asserted-by":"crossref","unstructured":"A. Sharma ,A. Sankaranarayanan. On the average behavior of the Fourier coefficients of $$j$$th symmetric power $$L$$-function over certain sequences of positive integers. Czechoslovak Math. J., 73(148)(3):885\u2013901, 2023","DOI":"10.21136\/CMJ.2023.0348-22"},{"issue":"2","key":"666_CR20","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/s00013-013-0481-8","volume":"100","author":"H Tang","year":"2013","unstructured":"H. Tang, Estimates for the Fourier coefficients of symmetric square $$L$$-functions. Arch. Math. (Basel) 100(2), 123\u2013130 (2013)","journal-title":"Arch. Math. (Basel)"}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-025-00666-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10998-025-00666-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-025-00666-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T14:30:50Z","timestamp":1763389850000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10998-025-00666-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,22]]},"references-count":20,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["666"],"URL":"https:\/\/doi.org\/10.1007\/s10998-025-00666-w","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"type":"print","value":"0031-5303"},{"type":"electronic","value":"1588-2829"}],"subject":[],"published":{"date-parts":[[2025,7,22]]},"assertion":[{"value":"17 December 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 July 2025","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}