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PreprintCC BY 4.0arXiv

A converse theorem for GL(2) over global fields without root numbers

  • Shantanu Agarwal
  • Muthu Krishnamurthy
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Abstract

We prove a converse theorem for GL(2) over global fields in which the root numbers in the twisted functional equations need not be prescribed. Instead, we allow nonzero scalar factors that are invariant under unramified twists. We show that these scalars are independent of the twisting character and obtain a unique isobaric automorphic representation with the prescribed unramified local components.

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Cite

BibTeXRIS
BibTeX
@misc{agarwal2026converse,
  title = {{A converse theorem for GL(2) over global fields without root numbers}},
  author = {Shantanu Agarwal and Muthu Krishnamurthy},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02217},
  eprint = {2611.02217},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02217},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A converse theorem for GL(2) over global fields without root numbers
AU  - Shantanu Agarwal
AU  - Muthu Krishnamurthy
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.02217
UR  - https://arxiv.org/abs/2611.02217
AB  - We prove a converse theorem for GL(2) over global fields in which the root numbers in the twisted functional equations need not be prescribed. Instead, we allow nonzero scalar factors that are invariant under unramified twists. We show that these scalars are independent of the twisting character and obtain a unique isobaric automorphic representation with the prescribed unramified local components.
ER  -