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arXiv · 2503.01575

Transcendence criteria for infinite products of algebraic numbers

Mathias L. Laursen
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Abstract

Using an application of Schmidt's Subspace Theorem, this paper gives new transcendence criteria for rapidly converging infinite products of algebraic numbers. The paper also improves existing criteria for irrationality of products and criteria for irrationality and transcendence of infinite series. These results generalize a classical theorem on the irrationality of infinite series due to Erd\H{o}s.

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Mathias L. Laursen. 2025-03-03. Transcendence criteria for infinite products of algebraic numbers. https://arxiv.org/abs/2503.01575

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