Abstract
In the first part theorems ofBaker are used to prove the transcendence of special values of power series whose coefficients are values of certain ordinary Dirichlet series with coefficients forming a periodic sequence of algebraic numbers. Especially the transcendence of Ψ(z)+C is shown for all rationalz which are not integers, Ψ denoting the logarithmic derivative of the gamma function andC Euler's constant. In the second part the intimate connection betweenSchanuel's conjecture and the arithmetic nature of\(\sum\limits_{n = 2}^\infty {\gamma (n)n^{ - s} }\),s=3,4,5... is studied where γ (n) denotes the number of distinct representation ofn in the forma b with positive integersa, b. This function was recently introduced byGolomb.
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Bundschuh, P. Zwei Bemerkungen über transzendente Zahlen. Monatshefte für Mathematik 88, 293–304 (1979). https://doi.org/10.1007/BF01534248
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DOI: https://doi.org/10.1007/BF01534248