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arXiv · 2301.02838

Congruences of the $q$-Fibonacci sequence related with its transcendence

Takumi Anzawa·Hidetaka Funakura
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Abstract

By using Andrews's explicit formulae of the $q$-Fibonacci sequence introduced by Schur, we prove certain congruences of the $q$-Fibonacci sequence which relate the sequence with the original Fibonacci sequence. As a corollary, we show that it yields a transcendental element in the $\mathbb{Q}$-algebra $\mathscr{A}$ of integers modulo infinitely large primes under the generalized Riemann hypothesis.

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Takumi Anzawa, Hidetaka Funakura. 2023-01-07. Congruences of the $q$-Fibonacci sequence related with its transcendence. https://arxiv.org/abs/2301.02838

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