Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 29 min ago
PreprintarXiv licencearXiv

A new way integral for the n-fold cover of SL2

  • Tianxiang Liu
Open at sourcePDFDOICite

Abstract

Let π be a genuine irreducible cuspidal automorphic representation of the n-fold cover SL2(n)(𝔸) of SL2(𝔸), n ≥ 3 odd, and let τ be the genuine representation of GL1(n)(𝔸) obtained from a unitary Hecke character of 𝔸×. We prove that, for a certain choice of data, a new way integral for SL2(n)(𝔸) represents the partial L-function LS(ns+1/2,π×τ). The integral is derived from the generalized doubling integral of Cai, Friedberg, Ginzburg and Kaplan, following the idea of Ginzburg and Soudry.

Related

  1. K-stability and birational rigidity of Fano 3-fold weighted complete intersections
    Takuzo Okada
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. The classification of smooth 3-fold flops
    Gavin Brown, Michael Wemyss
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. The taming of 3-fold flops
    Michael Wemyss
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. A note on the non-wandering dynamics in the n-fold symmetric products
    Maša Đorić
    arXivPreprintCC BY-SA 4.0Full textDynamical systemsarXiv
  5. A vertex operator algebra for the S-fold realisation of a non-unitary Haagerup--Izumi modular fusion category
    David E Evans
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{liu2026integral,
  title = {{A new way integral for the $n$-fold cover of $SL_2$}},
  author = {Tianxiang Liu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19110},
  eprint = {2610.19110},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19110},
}
RIS
TY  - UNPB
TI  - A new way integral for the n-fold cover of SL_2
AU  - Tianxiang Liu
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.19110
UR  - https://arxiv.org/abs/2610.19110
AB  - Let π be a genuine irreducible cuspidal automorphic representation of the n-fold cover SL_2^(n)(𝔸) of SL_2(𝔸), n ≥ 3 odd, and let τ be the genuine representation of GL_1^(n)(𝔸) obtained from a unitary Hecke character of 𝔸^×. We prove that, for a certain choice of data, a new way integral for SL_2^(n)(𝔸) represents the partial L-function L^S(ns+1/2,π×τ). The integral is derived from the generalized doubling integral of Cai, Friedberg, Ginzburg and Kaplan, following the idea of Ginzburg and Soudry.
ER  -