Open Research Index

An explicit rational-base irrationality region for Zudilin's Lambert series

Will Cook

Palomar Registrypalomar/PALOMAR-2026-10-22-000039Oct 22, 2026math.NTscore 0

For coprime integers a > b >= 1 satisfying b^μ < a, equivalently log b / log a < θ*, the selected Lean theorems prove irrationality of F(a/b). They include the base 31/4 and every positive integer power, plus associated irrationality-measure bounds. The region excludes 3/2. This configuration does not select the paper's later sharp fixed-base asymptotic or all-rank Hankel results.

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