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PreprintCC BY 4.0arXiv

v-adic Chowla-Selberg formula over function fields

  • Fu-Tsun Wei
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Abstract

Let v be a finite place of a rational function field with finite constant field. We establish an Ogus-type v-adic Chowla-Selberg formula for t-motives with "complex multiplication" by subfields of Carlitz cyclotomic function fields. For this purpose, we first introduce the v-adic crystalline action of the Weil group on the de Rham spaces of t-motives via the de Rham-crystalline comparison isomorphism of Hartl-Kim, and use it to give a "v-isocrystal" period interpretation of special values of Thakur's v-adic geometric gamma function. Our Ogus-type formula is then based on the isogeny theorem for CM t-motives, together with a recipe for constructing "abelian CM types" given in the ∞-adic setting over function fields.

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Cite

BibTeXRIS
BibTeX
@misc{wei2026vadic,
  title = {{$v$-adic Chowla-Selberg formula over function fields}},
  author = {Fu-Tsun Wei},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23287},
  eprint = {2609.23287},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23287},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - v-adic Chowla-Selberg formula over function fields
AU  - Fu-Tsun Wei
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23287
UR  - https://arxiv.org/abs/2609.23287
AB  - Let v be a finite place of a rational function field with finite constant field. We establish an Ogus-type v-adic Chowla-Selberg formula for t-motives with "complex multiplication" by subfields of Carlitz cyclotomic function fields. For this purpose, we first introduce the v-adic crystalline action of the Weil group on the de Rham spaces of t-motives via the de Rham-crystalline comparison isomorphism of Hartl-Kim, and use it to give a "v-isocrystal" period interpretation of special values of Thakur's v-adic geometric gamma function. Our Ogus-type formula is then based on the isogeny theorem for CM t-motives, together with a recipe for constructing "abelian CM types" given in the ∞-adic setting over function fields.
ER  -