Theta lifts of Bianchi modular forms and applications to paramodularity

BERGER, TOBIAS; DEMBÉLÉ, LASSINA; PACETTI, ARIEL; ŞENGÜN, MEHMET HALUK

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

OXFORD UNIV PRESS

Lugar: Oxford; Año: 2015 vol. 92 p. 353 - 370

0024-6107

We explain how the work of Johnson-Leung and Roberts on lifting Hilbert modular forms for real quadratic fields to Siegel modular forms can be adapted to imaginary quadratic fields. For this we use archimedean results from [HST93] and replace the global arguments of [Rob01] by the non-vanishing result of Takeda [Tak09].As an application of our lifting result, we exhibit an abelian surface B defined over Q, which is not restriction of scalars of an elliptic curve andsatisfies the Brumer-Kramer Paramodularity Conjecture [BK14].