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What is Fibonacci Zeta Function and Transcendence about?

The document discusses the Fibonacci zeta function, a lacunary Dirichlet series formed from the reciprocals of Fibonacci numbers raised to the s-th power, which has an analytic continuation to the entire complex plane. It explores the nature of its special values, revealing that values at negative integers are algebraic, while those at positive even integers are transcendental, and presents simplified proofs of these results. The paper also highlights connections to modular forms and introduces new results

Author

jeongguk97.n

Language

EN