Timeline for Self-dual automorphic forms on $GL(4)$

7 events

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Jun 28, 2014 at 23:39	history	edited	NAME_IN_CAPS	CC BY-SA 3.0	added 142 characters in body
Jun 28, 2014 at 23:38	comment	added	NAME_IN_CAPS		There is also the Yoshida lift on classical modular forms $f,g$, whose Andrianov/spinor $L$-function is $L(s-1,f)L(s,g)$ and whose standard $L$-function is $\zeta(s)L(s-2,f\otimes g)$, at least under certain circumstances. See the last paragraph (and indeed all of) Section 3 of dx.doi.org/10.1016/j.jnt.2006.11.005
Jun 28, 2014 at 23:16	history	edited	NAME_IN_CAPS	CC BY-SA 3.0	added 89 characters in body
Jun 28, 2014 at 23:15	comment	added	NAME_IN_CAPS		It seems that Saito-Kurokawa lift $F$ of a classical modular form $f$ has $L(s,F)=\zeta(s-k+1)\zeta(s-k+2)L(s,f)$, so automorphically this is probably just taking the direct sum of two Tate twists of the trivial rep with the automorphic rep corresponding to $f$. Again I don't really know. The Ikeda lift generalizes this to higher degree, so is probably not relevant. Langlands has the S-K case as functorality, $PGL_2\times PGL_2\rightarrow PGSp_4$, coming from the $SL_2\times SL_2 \rightarrow Sp_4$ on $L$-groups, sect 3 sunsite.ubc.ca/DigitalMathArchive/Langlands/pdf/autoreps-ps.pdf
Jun 28, 2014 at 22:40	history	edited	NAME_IN_CAPS	CC BY-SA 3.0	added 36 characters in body
Jun 28, 2014 at 22:30	history	edited	NAME_IN_CAPS	CC BY-SA 3.0	added 1978 characters in body
Jun 28, 2014 at 22:12	history	answered	NAME_IN_CAPS	CC BY-SA 3.0