dc.contributor.author | Pitale, A | |
dc.contributor.author | Saha, A | |
dc.contributor.author | Schmidt, R | |
dc.date.accessioned | 2020-04-08T13:04:50Z | |
dc.date.available | 2020-03-25 | |
dc.date.available | 2020-04-08T13:04:50Z | |
dc.date.issued | 2020 | |
dc.identifier.issn | 2195-4755 | |
dc.identifier.uri | https://qmro.qmul.ac.uk/xmlui/handle/123456789/63530 | |
dc.description.abstract | We prove an explicit integral representation -- involving the pullback of a suitable Siegel Eisenstein series -- for the twisted standard $L$-function associated to a holomorphic vector-valued Siegel cusp form of degree $n$ and arbitrary level. In contrast to all previously proved pullback formulas in this situation, our formula involves only scalar-valued functions despite being applicable to $L$-functions of vector-valued Siegel cusp forms. The key new ingredient in our method is a novel choice of local vectors at the archimedean place which allows us to exactly compute the archimedean local integral. By specializing our integral representation to the case $n=2$ we are able to prove a reciprocity law -- predicted by Deligne's conjecture -- for the critical special values of the twisted standard $L$-function for vector-valued Siegel cusp forms of degree 2 and arbitrary level. This arithmetic application generalizes previously proved critical-value results for the full level case. By specializing further to the case of Siegel cusp forms obtained via the Ramakrishnan--Shahidi lift, we obtain a reciprocity law for the critical special values of the symmetric fourth $L$-function of a classical newform. | en_US |
dc.publisher | Springer (part of Springer Nature) | en_US |
dc.relation.ispartof | Annales mathématiques du Québec | |
dc.rights | This is a pre-copyedited, author-produced version of an article accepted for publication in Annales mathématiques du Québec following peer review. | |
dc.subject | math.NT | en_US |
dc.subject | math.NT | en_US |
dc.title | On the standard $L$-function for $GSp_{2n} \times GL_1$ and algebraicity of symmetric fourth $L$-values for $GL_2$ | en_US |
dc.type | Article | en_US |
dc.rights.holder | © 2020 Springer (part of Springer Nature) | |
pubs.author-url | http://arxiv.org/abs/1803.06227v3 | en_US |
pubs.notes | Not known | en_US |
pubs.publication-status | Accepted | en_US |
dcterms.dateAccepted | 2020-03-25 | |
rioxxterms.funder | Default funder | en_US |
rioxxterms.identifier.project | Default project | en_US |