{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T17:38:29Z","timestamp":1776793109976,"version":"3.51.2"},"reference-count":23,"publisher":"American Mathematical Society (AMS)","issue":"273","license":[{"start":{"date-parts":[[2011,4,15]],"date-time":"2011-04-15T00:00:00Z","timestamp":1302825600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We obtain formulas for certain weighted sums of values of the symmetric square and triple product\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L\">\n                        <mml:semantics>\n                          <mml:mi>L<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">L<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -functions. As a consequence, we get exact values at the right critical point for the symmetric square and symmetric cube\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L\">\n                        <mml:semantics>\n                          <mml:mi>L<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">L<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -functions attached to certain cuspforms. We also give applications to Fourier coefficients of modular forms.\n                  <\/p>","DOI":"10.1090\/s0025-5718-10-02350-1","type":"journal-article","created":{"date-parts":[[2010,10,4]],"date-time":"2010-10-04T11:01:54Z","timestamp":1286190114000},"page":"409-428","source":"Crossref","is-referenced-by-count":4,"title":["Values of symmetric cube \ud835\udc3f-functions and Fourier coefficients of Siegel Eisenstein series of degree-3"],"prefix":"10.1090","volume":"80","author":[{"given":"Dominic","family":"Lanphier","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2010,4,15]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1007\/BF01158040","article-title":"\u00dcber die Fourierkoeffizienten der Siegelschen Eisensteinreihen","volume":"45","author":"B\u00f6cherer, Siegfried","year":"1984","journal-title":"Manuscripta Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-2611","issn-type":"print"},{"key":"2","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1515\/crll.1985.362.146","article-title":"\u00dcber die Funktionalgleichung automorpher \ud835\udc3f-Funktionen zur Siegelschen Modulgruppe","volume":"362","author":"B\u00f6cherer, Siegfried","year":"1985","journal-title":"J. Reine Angew. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0075-4102","issn-type":"print"},{"issue":"3","key":"3","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/BF01436180","article-title":"Sums involving the values at negative integers of \ud835\udc3f-functions of quadratic characters","volume":"217","author":"Cohen, Henri","year":"1975","journal-title":"Math. Ann.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5831","issn-type":"print"},{"issue":"8","key":"4","doi-asserted-by":"publisher","first-page":"2283","DOI":"10.1090\/S0002-9939-96-03334-5","article-title":"On Ramanujan congruences for modular forms of integral and half-integral weights","volume":"124","author":"Datskovsky, B.","year":"1996","journal-title":"Proc. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9939","issn-type":"print"},{"key":"5","isbn-type":"print","first-page":"313","article-title":"Valeurs de fonctions \ud835\udc3f et p\u00e9riodes d\u2019int\u00e9grales","author":"Deligne, P.","year":"1979","ISBN":"https:\/\/id.crossref.org\/isbn\/0821814370"},{"issue":"3","key":"6","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1080\/10586458.2001.10504458","article-title":"Symmetric square \ud835\udc3f-functions and Shafarevich-Tate groups","volume":"10","author":"Dummigan, Neil","year":"2001","journal-title":"Experiment. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/1058-6458","issn-type":"print"},{"key":"7","series-title":"Progress in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9162-3","volume-title":"The theory of Jacobi forms","volume":"55","author":"Eichler, Martin","year":"1985","ISBN":"https:\/\/id.crossref.org\/isbn\/0817631801"},{"key":"8","isbn-type":"print","first-page":"114","article-title":"Pullbacks of Eisenstein series; applications","author":"Garrett, Paul B.","year":"1984","ISBN":"https:\/\/id.crossref.org\/isbn\/0817631720"},{"key":"9","isbn-type":"print","first-page":"241","article-title":"Integral representations of Eisenstein series and \ud835\udc3f-functions","author":"Garrett, Paul B.","year":"1989","ISBN":"https:\/\/id.crossref.org\/isbn\/0120675706"},{"issue":"2","key":"10","doi-asserted-by":"publisher","first-page":"209","DOI":"10.2307\/1971310","article-title":"Decomposition of Eisenstein series: Rankin triple products","volume":"125","author":"Garrett, Paul B.","year":"1987","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"issue":"3","key":"11","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1007\/BF01231899","article-title":"On the arithmetic of Siegel-Hilbert cuspforms: Petersson inner products and Fourier coefficients","volume":"107","author":"Garrett, Paul B.","year":"1992","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","issn-type":"print"},{"issue":"1","key":"12","doi-asserted-by":"publisher","first-page":"161","DOI":"10.2307\/2374726","article-title":"Special values of triple product \ud835\udc3f-functions","volume":"115","author":"Garrett, Paul B.","year":"1993","journal-title":"Amer. J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9327","issn-type":"print"},{"issue":"265","key":"13","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1090\/S0025-5718-08-02136-4","article-title":"Congruences for the Ramanujan function and generalized class numbers","volume":"78","author":"Heim, Bernhard","year":"2009","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"14","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1017\/S0027763000006267","article-title":"An explicit formula for the Fourier coefficients of Siegel-Eisenstein series of degree 3","volume":"146","author":"Katsurada, Hidenori","year":"1997","journal-title":"Nagoya Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/0027-7630","issn-type":"print"},{"issue":"1","key":"15","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1080\/10586458.2005.10128910","article-title":"Special values of the standard zeta functions for elliptic modular forms","volume":"14","author":"Katsurada, Hidenori","year":"2005","journal-title":"Experiment. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/1058-6458","issn-type":"print"},{"issue":"2","key":"16","doi-asserted-by":"publisher","first-page":"645","DOI":"10.2307\/121091","article-title":"Symmetric cube \ud835\udc3f-functions for \ud835\udc3a\ud835\udc3f\u2082 are entire","volume":"150","author":"Kim, Henry H.","year":"1999","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"key":"17","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1007\/BF02834847","article-title":"Holomorphy of Rankin triple \ud835\udc3f-functions; special values and root numbers for symmetric cube \ud835\udc3f-functions","volume":"120","author":"Kim, Henry H.","year":"2000","journal-title":"Israel J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-2172","issn-type":"print"},{"key":"18","series-title":"Cambridge Studies in Advanced Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511619878","volume-title":"Introductory lectures on Siegel modular forms","volume":"20","author":"Klingen, Helmut","year":"1990","ISBN":"https:\/\/id.crossref.org\/isbn\/0521350522"},{"key":"19","series-title":"Lecture Notes in Mathematics, Vol. 216","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0058625","volume-title":"Siegel's modular forms and Dirichlet series","author":"Maass, Hans","year":"1971"},{"key":"20","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/BF02940913","article-title":"Special values of triple product \ud835\udc3f-functions and nearly holomorphic Eisenstein series","volume":"70","author":"Mizumoto, S.","year":"2000","journal-title":"Abh. Math. Sem. Univ. Hamburg","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5858","issn-type":"print"},{"issue":"6","key":"21","first-page":"252","article-title":"Table of the Fourier coefficients of Eisenstein series of degree 3","volume":"59","author":"Ozeki, Michio","year":"1983","journal-title":"Proc. Japan Acad. Ser. A Math. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0386-2194","issn-type":"print"},{"issue":"3","key":"22","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1007\/BF01391466","article-title":"On the periods of modular forms","volume":"229","author":"Shimura, Goro","year":"1977","journal-title":"Math. Ann.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5831","issn-type":"print"},{"key":"23","isbn-type":"print","first-page":"105","article-title":"Modular forms whose Fourier coefficients involve zeta-functions of quadratic fields","author":"Zagier, D.","year":"1977","ISBN":"https:\/\/id.crossref.org\/isbn\/3540085300"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2011-80-273\/S0025-5718-10-02350-1\/S0025-5718-10-02350-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2011-80-273\/S0025-5718-10-02350-1\/S0025-5718-10-02350-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:41:37Z","timestamp":1776789697000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2011-80-273\/S0025-5718-10-02350-1\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,4,15]]},"references-count":23,"journal-issue":{"issue":"273","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["S0025-5718-10-02350-1"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-10-02350-1","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2010,4,15]]}}}