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https://doi.org/10.3336/gm.53.2.03

On Poincaré series of half-integral weight

Sonja Žunar ; Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia

Puni tekst: engleski, pdf (251 KB) str. 239-264 preuzimanja: 189* citiraj
APA 6th Edition
Žunar, S. (2018). On Poincaré series of half-integral weight. Glasnik matematički, 53 (2), 239-264. https://doi.org/10.3336/gm.53.2.03
MLA 8th Edition
Žunar, Sonja. "On Poincaré series of half-integral weight." Glasnik matematički, vol. 53, br. 2, 2018, str. 239-264. https://doi.org/10.3336/gm.53.2.03. Citirano 16.10.2021.
Chicago 17th Edition
Žunar, Sonja. "On Poincaré series of half-integral weight." Glasnik matematički 53, br. 2 (2018): 239-264. https://doi.org/10.3336/gm.53.2.03
Harvard
Žunar, S. (2018). 'On Poincaré series of half-integral weight', Glasnik matematički, 53(2), str. 239-264. https://doi.org/10.3336/gm.53.2.03
Vancouver
Žunar S. On Poincaré series of half-integral weight. Glasnik matematički [Internet]. 2018 [pristupljeno 16.10.2021.];53(2):239-264. https://doi.org/10.3336/gm.53.2.03
IEEE
S. Žunar, "On Poincaré series of half-integral weight", Glasnik matematički, vol.53, br. 2, str. 239-264, 2018. [Online]. https://doi.org/10.3336/gm.53.2.03

Sažetak
We use Poincaré series of K -finite matrix coefficients of genuine integrable representations of the metaplectic cover of SL2(ℝ) to construct a spanning set for the space of cusp forms Sm(Γ,χ) , where Γ is a discrete subgroup of finite covolume in the metaplectic cover of SL2(ℝ) , χ is a character of Γ of finite order, and m5/2+ℤ≥0 . We give a result on the non-vanishing of the constructed cusp forms and compute their Petersson inner product with any f Sm(Γ,χ) . Using this last result, we construct a Poincaré series ΔΓ,k,m,ξ,χ Sm(Γ,χ) that corresponds, in the sense of the Riesz representation theorem, to the linear functional f ↦ f(k)(ξ) on Sm(Γ,χ) , where ξℂℑ(z)>0 and kℤ≥0 . Under some additional conditions on Γ and χ , we provide the Fourier expansion of cusp forms ΔΓ,k,m,ξ,χ and their expansion in a series of classical Poincaré series.

Ključne riječi
Cusp forms of half-integral weight; Poincaré series; metaplectic cover of SL2(ℝ)

Hrčak ID: 214474

URI
https://hrcak.srce.hr/214474

Posjeta: 339 *