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Twisting-free converse theorems for Γ0(32) and Γ0(36)

  • Pengcheng Zhang
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Abstract

We prove twisting-free converse theorems for Γ0(32) and Γ0(36) under the setting of Conrey--Farmer, namely assuming a single functional equation and a suitable Euler product, with particular shapes at ramified primes. The proofs make substantial use of the ramified primes, with methods somewhat different from the existing ones in the literature.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026twistingfree,
  title = {{Twisting-free converse theorems for $Γ_0(32)$ and $Γ_0(36)$}},
  author = {Pengcheng Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00850},
  eprint = {2611.00850},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00850},
}
RIS
TY  - UNPB
TI  - Twisting-free converse theorems for Γ_0(32) and Γ_0(36)
AU  - Pengcheng Zhang
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00850
UR  - https://arxiv.org/abs/2611.00850
AB  - We prove twisting-free converse theorems for Γ_0(32) and Γ_0(36) under the setting of Conrey--Farmer, namely assuming a single functional equation and a suitable Euler product, with particular shapes at ramified primes. The proofs make substantial use of the ramified primes, with methods somewhat different from the existing ones in the literature.
ER  -