PreprintCC BY 4.0arXiv
Finite-slope p-adic L-functions for GL3
Abstract
Let Π be a regular algebraic cuspidal automorphic representation of GL3(𝔸ℚ) of weight $(a, 0, -a)$, and let p be a prime. Generalising work of Loeffler--Williams in the nearly-ordinary case, we construct p-adic L-functions for each small slope regular P1-refinement of Π at p consistent with the conjectures of Coates--Perrin-Riou and Panchishkin.
Related
- On the syntomic regulator of the Hesse cubic curves and p-adic hypergeometric functions
- Iwasawa invariants of sharp/flat $2$-adic L-functions for quadratic twists of elliptic curves
- Bounds for (k,c) model functions over p-adic fields
- p-adic spectral zeta functions via the inverse Stieltjes transform
- p-adic properties of division polynomials and algebraic sigma functions
BibTeX
@misc{dimitrakopoulou2026finiteslope,
title = {{Finite-slope p-adic L-functions for $\mathrmGL_3$}},
author = {Xenia Dimitrakopoulou and Rob Rockwood},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.39539},
eprint = {2609.39539},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39539},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finite-slope p-adic L-functions for GL_3
AU - Xenia Dimitrakopoulou
AU - Rob Rockwood
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2609.39539
UR - https://arxiv.org/abs/2609.39539
AB - Let Π be a regular algebraic cuspidal automorphic representation of GL_3(𝔸_ℚ) of weight $(a, 0, -a)$, and let p be a prime. Generalising work of Loeffler--Williams in the nearly-ordinary case, we construct p-adic L-functions for each small slope regular P_1-refinement of Π at p consistent with the conjectures of Coates--Perrin-Riou and Panchishkin.
ER -