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arXiv · 2610.40698

A Diophantine generalization of Fourier's irrationality trick

Archan Chattopadhyay·Chandan Chattopadhyay
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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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Archan Chattopadhyay, Chandan Chattopadhyay. 2026-10-28. A Diophantine generalization of Fourier's irrationality trick. https://doi.org/10.1080/00255572.2026.2748847

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