Transcendence of Periods: The State of the Art

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Elliptic Functions and Transcendence (2008, background): “W¨ustholz [245] have shown that the only linear dependence relations with algebraic coefﬁcients between the values B ( a , b ) of the Euler beta function at points ( a , b ) ∈ Q 2 are those that follow from the Deligne–Koblitz–Ogus relations (see further references in [243]).”
Euler's constant: Euler's work and modern developments (2013, background): “The state of the art for showing transcendence of periods is surveyed by Waldschmidt [312].”
Diagonalization and Rationalization of algebraic Laurent series (2012, background): “Introduction A very rich interplay between arithmetic, geometry, transcendence and combinatorics arises in the study of homogeneous linear differential equations and especially of those that “come from geometry” and the related study of Siegel G-functions (see for instance [4, 16, 23, 30, 31, 33] fo”
Transcendental values of the digamma function (2007, background): “For a detailed exposition of the “state of the art,” we suggest Waldschmidt [21].”