A multivariate integral representation on $\mathrm {GL}_2 \times \mathrm {GSp}_4$ inspired by the pullback formula
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- by Aaron Pollack and Shrenik Shah PDF
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Abstract:
We give a two variable Rankin–Selberg integral inspired by consideration of Garrett’s pullback formula. For a globally generic cusp form on $\mathrm {GL}_2\times \mathrm {GSp}_4$, the integral represents the product of the $\mathrm {Std}\times \mathrm {Spin}$ and $\mathbf {1} \times \mathrm {Std}$ $L$-functions. We prove a result concerning an Archimedean principal series representation in order to verify a case of Jiang’s first-term identity relating certain non-Siegel Eisenstein series on symplectic groups. Using it, we obtain a new proof of a known result concerning possible poles of these $L$-functions.References
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Additional Information
- Aaron Pollack
- Affiliation: Department of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
- MR Author ID: 1217139
- ORCID: 0000-0001-9240-0762
- Email: aaronjp@math.ias.edu
- Shrenik Shah
- Affiliation: Department of Mathematics, Columbia University, New York 10027
- MR Author ID: 869328
- Email: snshah@math.columbia.edu
- Received by editor(s): July 10, 2017
- Received by editor(s) in revised form: November 9, 2017, and November 11, 2017
- Published electronically: August 22, 2018
- Additional Notes: The first author has been supported by NSF grant DMS-1401858.
The second author has been supported by NSF grant DMS-1401967. - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 5591-5630
- MSC (2010): Primary 11F46, 11F66, 11F70
- DOI: https://doi.org/10.1090/tran/7463
- MathSciNet review: 3937304