Modular forms for the $$A_{1}$$ A 1 -tower

Woitalla, Martin

doi:10.1007/s12188-018-0197-6

Cited by 3 publications

(2 citation statements)

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“…considered by Woitalla in [72], who proved that the algebra M * (O + (2U ⊕ 4A 1 )) at the top is freely generated in weights 4, 4, 6, 6, 8, 10, 12. The bottom of the tower is the famous Igusa algebra [38] of Siegel modular forms of degree two and even weight which is freely generated in weights 4, 6, 10, 12.…”

Section: 4mentioning

confidence: 99%

Modular forms with poles on hyperplane arrangements

Wang¹,

Williams²

2021

Preprint

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We study algebras of meromorphic modular forms whose poles lie on Heegner divisors for orthogonal and unitary groups associated to root lattices. We give a uniform construction of 147 hyperplane arrangements on type IV symmetric domains for which the algebras of modular forms with constrained poles are free and therefore the Looijenga compactifications of the arrangement complements are weighted projective spaces. We also construct 8 free algebras of modular forms on complex balls with poles on hyperplane arrangements. The most striking example is the discriminant kernel of the 2U ⊕ D11 lattice, which admits a free algebra on 14 meromorphic generators. Along the way, we determine minimal systems of generators for non-free algebras of orthogonal modular forms for 26 reducible root lattices and prove the modularity of formal Fourier-Jacobi series associated to them. By exploiting an identity between weight one singular additive and multiplicative lifts on 2U ⊕ D11, we prove that the additive lift of any (possibly weak) theta block of positive weight and q-order one is a Borcherds product; the special case of holomorphic theta blocks of one elliptic variable is the theta block conjecture of Gritsenko, Poor and Yuen.

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Section: 4mentioning

confidence: 99%

Modular forms with poles on hyperplane arrangements

Wang¹,

Williams²

2021

Preprint

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“…The B 4 case was studied in [Kri11]. The B n -tower was also considered systematically in [Woi18]. Krieg [Kri05] worked out the D 4 case in the context of quaternionic modular forms.…”

Section: Introductionmentioning

confidence: 99%