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PreprintarXiv licencearXiv

On the absolute convergence of the spectral side of the twisted trace formula

  • Werner Müller
  • Satoshi Wakatsuki
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Abstract

We establish the absolute convergence of the spectral side of the twisted trace formula for reductive algebraic groups. More precisely, we extend the absolute convergence theorem of the spectral side due to Finis--Lapid--Müller to the twisted setting. This paper provides a detailed proof of the absolute convergence theorem, whose proof is known to experts but does not seem to have appeared in the literature. The resulting formulas are motivated by applications to limit multiplicity problems and to Weyl laws for self-dual automorphic representations of GLn.

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Cite

BibTeXRIS
BibTeX
@misc{muller2026absolute,
  title = {{On the absolute convergence of the spectral side of the twisted trace formula}},
  author = {Werner Müller and Satoshi Wakatsuki},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.18870},
  eprint = {2607.18870},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.18870},
}
RIS
TY  - UNPB
TI  - On the absolute convergence of the spectral side of the twisted trace formula
AU  - Werner Müller
AU  - Satoshi Wakatsuki
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2607.18870
UR  - https://arxiv.org/abs/2607.18870
AB  - We establish the absolute convergence of the spectral side of the twisted trace formula for reductive algebraic groups. More precisely, we extend the absolute convergence theorem of the spectral side due to Finis--Lapid--Müller to the twisted setting. This paper provides a detailed proof of the absolute convergence theorem, whose proof is known to experts but does not seem to have appeared in the literature. The resulting formulas are motivated by applications to limit multiplicity problems and to Weyl laws for self-dual automorphic representations of GL_n.
ER  -