Many beautiful results on the value-distribution of L-functions follow from the general theory of Dirichlet series like the Big Picard theorem (see Boas [26] and Mandelbrojt [234]), but more advanced statements can only be proved by exploiting the characterizing properties (the functional equation and the Euler product). In this chapter, we study the distribution of values of Dirichlet series satisfying a Riemann-type functional equation. These results are due to Steuding [346, 347] and their proofs follow in the main part the methods of Levinson [217], Levinson and Montgomery [218], and Nevanlinna theory.
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© 2007 Springer-Verlag Berlin Heidelberg
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(2007). Value-Distribution in the Complex Plane. In: Value-Distribution of L-Functions. Lecture Notes in Mathematics, vol 1877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44822-8_7
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DOI: https://doi.org/10.1007/978-3-540-44822-8_7
Publisher Name: Springer, Berlin, Heidelberg
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