A BÖCHERER-TYPE CONJECTURE FOR PARAMODULAR FORMS
2011 ◽
Vol 07
(05)
◽
pp. 1395-1411
◽
Keyword(s):
In the 1980s Böcherer formulated a conjecture relating the central value of the quadratic twists of the spinor L-function attached to a Siegel modular form F to the coefficients of F. He proved the conjecture when F is a Saito–Kurokawa lift. Later Kohnen and Kuß gave numerical evidence for the conjecture in the case when F is a rational eigenform that is not a Saito–Kurokawa lift. In this paper we develop a conjecture relating the central value of the quadratic twists of the spinor L-function attached to a paramodular form and the coefficients of the form. We prove the conjecture in the case when the form is a Gritsenko lift and provide numerical evidence when it is not a lift.
Keyword(s):
2010 ◽
Vol 13
◽
pp. 192-207
◽
Keyword(s):
1997 ◽
Vol 147
◽
pp. 71-106
◽
2002 ◽
Vol 65
(2)
◽
pp. 239-252
◽
2018 ◽
Vol 168
(1)
◽
pp. 197-209
◽
Keyword(s):
2008 ◽
Vol 04
(05)
◽
pp. 735-746
◽
Keyword(s):
Keyword(s):