PreprintCC BY 4.0arXiv
A Diophantine generalization of Fourier's irrationality trick
Abstract
We revisit Fourier's method for proving the irrationality of e and generalize it into a unified Diophantine framework, which applies to a broad class of series with bounded or mildly growing integer numerators, and suitably growing, divisible denominators. Using integer linear forms, we establish a general criterion that recovers classical irrationality results while also generating new ones within a single structural approach.
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BibTeX
@misc{chattopadhyay2026diophantine,
title = {{A Diophantine generalization of Fourier's irrationality trick}},
author = {Archan Chattopadhyay and Chandan Chattopadhyay},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40698},
eprint = {2610.40698},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40698},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Diophantine generalization of Fourier's irrationality trick
AU - Archan Chattopadhyay
AU - Chandan Chattopadhyay
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.40698
UR - https://arxiv.org/abs/2610.40698
AB - We revisit Fourier's method for proving the irrationality of e and generalize it into a unified Diophantine framework, which applies to a broad class of series with bounded or mildly growing integer numerators, and suitably growing, divisible denominators. Using integer linear forms, we establish a general criterion that recovers classical irrationality results while also generating new ones within a single structural approach.
ER -