Resumen de Integrality and cuspidality of pullbacks of nearly holomorphic Siegel Eisenstein series

Ameya Pitale, Abhishek Saha, Ralf Schmidt

• We study nearly holomorphic Siegel Eisenstein series of general levels and characters on H2n, the Siegel upper half space of degree 2n. We prove that the Fourier coefficients of these Eisenstein series (once suitably normalized) lie in the ring of integers of Qp for all sufficiently large primes p. We also prove that the pullbacks of these Eisenstein series to Hn × Hn are cuspidal under certain assumptions.