Transfer of Siegel Cusp Forms of Degree 2 (eBook)

Ameya Pitale (Autor)

eBook Download: PDF

107 Seiten
American Mathematical Society (Verlag)
978-1-4704-1893-9 (ISBN)

Infos

Let $/pi$ be the automorphic representation of $/textrm{GSp}_4(/mathbb{A})$ generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and $/tau$ be an arbitrary cuspidal, automorphic representation of $/textrm{GL}_2(/mathbb{A})$. Using Furusawa's integral representation for $/textrm{GSp}_4/times/textrm{GL}_2$ combined with a pullback formula involving the unitary group $/textrm{GU}(3,3)$, the authors prove that the $L$-functions $L(s,/pi/times/tau)$ are "e;nice"e;. The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations $/pi$ have a functorial lifting to a cuspidal representation of $/textrm{GL}_4(/mathbb{A})$. Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of $/pi$ to a cuspidal representation of $/textrm{GL}_5(/mathbb{A})$. As an application, the authors obtain analytic properties of various $L$-functions related to full level Siegel cusp forms. They also obtain special value results for $/textrm{GSp}_4/times/textrm{GL}_1$ and $/textrm{GSp}_4/times/textrm{GL}_2$.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• ISBN-10: 1-4704-1893-2 / 1470418932
• ISBN-13: 978-1-4704-1893-9 / 9781470418939