Codimensions of the spaces of cusp forms for Siegel congruence subgroups in degree two

Shukla, Alok

doi:10.2140/pjm.2018.293.207

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Cited by 3 publications

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“…Since Φ p is supported only on Q(Q p )1Si(p np ) for each p|N, it follows from Lemma 7.2, [21], which essentially depends on the double coset decompositions of Q(Q)\ GSp(4, Q)/Γ 0 (p np ) as computed in [23], that only those γ will contribute in the summation for which…”

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confidence: 99%

Pullback of Klingen Eisenstein series and certain critical L-values identities

Shukla¹

2020

Preprint

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We obtain pullback formulas for Klingen Eisenstein series with arbitrary levels, with respect to both Siegel congruence and paramodular subgroups, in degree two. Pullback results are used, along with the Fourier series expansion of Klingen Eisenstein series given by Mizumoto, to prove certain identities involving critical values of L-functions attached to normalized elliptic modular forms of weight k and full level.

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confidence: 99%

Pullback of Klingen Eisenstein series and certain critical L-values identities

Shukla¹

2020

Preprint

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Pullback of Klingen Eisenstein series and certain critical L-values identities

Shukla

2020

Ramanujan J

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Dimension formulas for Siegel modular forms of level 4

Roy

Schmidt

2023

Mathematika

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We prove several dimension formulas for spaces of scalar-valued Siegel modular forms of degree 2 with respect to certain congruence subgroups of level 4.In case of cusp forms, all modular forms considered originate from cuspidal automorphic representations of GSp(4, 𝔸) whose local component at 𝑝 = 2 admits nonzero fixed vectors under the principal congruence subgroup of level 2. Using known dimension formulas combined with dimensions of spaces of fixed vectors in local representations at 𝑝 = 2, we obtain formulas for the number of relevant automorphic representations. These, in turn, lead to new dimension formulas, in particular for Siegel modular forms with respect to the Klingen congruence subgroup of level 4. M S C 2 0 2 0 11F46, 11F70 (primary) Contents

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Codimensions of the spaces of cusp forms for Siegel congruence subgroups in degree two

Cited by 3 publications

References 6 publications

Pullback of Klingen Eisenstein series and certain critical L-values identities

Pullback of Klingen Eisenstein series and certain critical L-values identities

Pullback of Klingen Eisenstein series and certain critical L-values identities

Dimension formulas for Siegel modular forms of level 4

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