Details

Autor(en) / Beteiligte

• Brown, Jim
• Geller, Hugh
• Vicente, Rico
• Walsh, Alexandra

Titel

Eigenform product identities for degree two Siegel modular forms

Ist Teil von

• Journal of number theory, 2019-11, Vol.204, p.25-40

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

2019

Quelle

Elsevier ScienceDirect Journals

Beschreibungen/Notizen

• It is known via work of Duke and Ghate that there are only finitely many pairs of full level, degree one eigenforms f and g whose product fg is also an eigenform. We prove a partial generalization of this theorem for degree two Siegel modular forms. Namely, we show that there is only one pair of eigenforms F and G such that FG is a non-cuspidal eigenform. In the case that FG is a cuspform, we provide necessary conditions for FG to be an eigenform, give one example, and conjecture that is the only example.