PreprintCC BY 4.0arXiv
The irrationality measure of π is at most 7.101862832357
Abstract
We introduce two independent numerator exponents into the Zeilberger--Zudilin integral and specialize them to A1=A2=1857/2785. The resulting integer linear forms in $1$ and π prove μ(π)<7.101862832357. This lowers the Zeilberger--Zudilin upper bound 7.103205334137… by more than $0.001342501780$; the difference between the unrounded bounds is 0.0013425017806509…, approximately 0.01890%. The same parameter point is a strict two-dimensional local minimizer of the explicit auxiliary upper-bound function in its admissible arithmetic chamber. This is a local statement about that function, not a claim that the point is a global optimizer among all constructions.
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BibTeX
@misc{bai2026irrationality,
title = {{The irrationality measure of π is at most 7.101862832357}},
author = {Yufei Bai},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11276},
eprint = {2609.11276},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11276},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The irrationality measure of π is at most 7.101862832357
AU - Yufei Bai
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.11276
UR - https://arxiv.org/abs/2609.11276
AB - We introduce two independent numerator exponents into the Zeilberger--Zudilin integral and specialize them to A_1=A_2=1857/2785. The resulting integer linear forms in $1$ and π prove μ(π)<7.101862832357. This lowers the Zeilberger--Zudilin upper bound 7.103205334137… by more than $0.001342501780$; the difference between the unrounded bounds is 0.0013425017806509…, approximately 0.01890%. The same parameter point is a strict two-dimensional local minimizer of the explicit auxiliary upper-bound function in its admissible arithmetic chamber. This is a local statement about that function, not a claim that the point is a global optimizer among all constructions.
ER -