The completed standard L-function of modular forms on G2

Show simple item record Cicek, Fatma Davidoff, Giuliana Dijols, Sarah Hammonds, Trajan Pollack, Aaron Roy, Manami 2021-05-14T05:18:45Z 2021-05-14T05:18:45Z 2021-04
dc.identifier.citation Cicek, Fatma; Davidoff, Giuliana; Dijols, Sarah; Hammonds, Trajan; Pollack, Aaron and Roy, Manami, “The completed standard L-function of modular forms on G2”, arXiv, Cornell University Library, DOI: arXiv:2104.09448, Apr. 2021. en_US
dc.description.abstract Modular forms on the split exceptional group G2 over Q are a special class of automorphic forms on this group, which were introduced by Gan, Gross, and Savin. If π is a cuspidal automorphic representation of G2(A) corresponding to a level one, even weight modular form φ on G2, we define an associated completed standard L-function, Λ(π,Std,s). Assuming that a certain Fourier coefficient of φ is nonzero, we prove the functional equation Λ(π,Std,s)=Λ(π,Std,1−s). The proof proceeds via a careful analysis of a Rankin-Selberg integral due to Gurevich and Segal.
dc.description.statementofresponsibility by Fatma, Cicek, Giuliana Davidoff, Sarah Dijols, Trajan Hammonds, Aaron Pollack and Manami Roy
dc.language.iso en_US en_US
dc.publisher Cornell University Library en_US
dc.subject Number Theory en_US
dc.subject Representation Theory en_US
dc.title The completed standard L-function of modular forms on G2 en_US
dc.type Pre-Print en_US
dc.relation.journal arXiv

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