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On Poincaré series of half-integral weight


Žunar, Sonja
On Poincaré series of half-integral weight // Glasnik matematički, 53 (2018), 2; 239-264 doi:10.3336/gm.53.2.03 (međunarodna recenzija, članak, znanstveni)


Naslov
On Poincaré series of half-integral weight

Autori
Žunar, Sonja

Izvornik
Glasnik matematički (0017-095X) 53 (2018), 2; 239-264

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Cusp forms of half-integral weight, Poincaré series, metaplectic cover of SL_2(R)

Sažetak
We use Poincaré series of K-finite matrix coefficients of genuine integrable representations of the metaplectic cover of SL_2(ℝ) to construct a spanning set for the space of cusp forms S_m(Γ, χ), where Γ is a discrete subgroup of finite covolume in the metaplectic cover of SL_2(ℝ), χ is a character of Γ of finite order, and m is in 5/2+ℤ_{; ; ≥0}; ; . We give a result on the non-vanishing of the constructed cusp forms and compute their Petersson inner product with any f in S_m(Γ, χ). Using this last result, we construct a Poincaré series Δ_{; ; Γ, k, m, ξ, χ}; ; in S_m(Γ, χ) that corresponds, in the sense of the Riesz representation theorem, to the linear functional f ↦ f^{; ; (k)}; ; (ξ) on S_m(Γ, χ), where ξ is in ℂ_{; ; ℑ(z)>0}; ; and k is in ℤ_{; ; ≥0}; ; . Under some additional conditions on Γ and χ, we provide the Fourier expansion of cusp forms Δ_{; ; Γ, k, m, ξ, χ}; ; and their expansion in a series of classical Poincaré series.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekt / tema
HRZZ-IP-2013-11-9364 - Automorfne forme, reprezentacije i primjene (Goran Muić, )

Ustanove
Prirodoslovno-matematički fakultet, Zagreb

Autor s matičnim brojem:
Sonja Žunar, (362921)

Časopis indeksira:


  • Current Contents Connect (CCC)
  • Web of Science Core Collection (WoSCC)
    • Science Citation Index Expanded (SCI-EXP)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus


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