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Products of vector valued Eisenstein series

Martin Westerholt-Raum (Institutionen för matematiska vetenskaper, Algebra och geometri)
Forum Mathematicum (0933-7741). Vol. 29 (2017), 1, p. 157-186.
[Artikel, refereegranskad vetenskaplig]

We prove that products of at most two vector valued Eisenstein series that originate in level 1 span all spaces of cusp forms for congruence subgroups. This can be viewed as an analogue in the level aspect to a result that goes back to Rankin, and Kohnen and Zagier, which focuses on the weight aspect. The main feature of the proof are vector valued Hecke operators. We recover several classical constructions from them, including classical Hecke operators, Atkin-Lehner involutions, and oldforms. As a corollary to our main theorem, we obtain a vanishing condition for modular forms reminiscent of period relations deduced by Kohnen and Zagier in the context their previously mentioned result.

Nyckelord: Vector valued Hecke operators, period relations, cusp expansions of modular forms, toric modular-forms, identities, weight, Mathematics



Denna post skapades 2017-02-08.
CPL Pubid: 248060

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, Algebra och geometriInstitutionen för matematiska vetenskaper, Algebra och geometri (GU)

Ämnesområden

Algebra och geometri

Chalmers infrastruktur