Kohji Matsumoto, Yoshio Tanigawa (2003)
Journal de théorie des nombres de Bordeaux
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Multiple Dirichlet series of several complex variables are considered. Using the Mellin-Barnes integral formula, we prove the analytic continuation and an upper bound estimate.
Abou-Tair, Ibrahim A. (1987)
International Journal of Mathematics and Mathematical Sciences
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Takashi Nakamura (2009)
Acta Arithmetica
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G. Molteni (2010)
Acta Arithmetica
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G. Molteni (2010)
Acta Arithmetica
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Uckath-Variyath Balakrishnan (1984)
Mathematische Zeitschrift
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W. L. Ferrar (1937)
Compositio Mathematica
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Balanzario, Eugenio P. (2000)
Divulgaciones Matemáticas
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Garunkštis, R., Laurinčikas, A. (1999)
Publications de l'Institut Mathématique. Nouvelle Série
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Takuya Okamoto, Tomokazu Onozuka (2015)
Acta Arithmetica
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We give a method of obtaining explicit formulas for various mean values of Dirichlet L-functions which are expressed in terms of the Riemann zeta-function, the Euler function and Jordan's totient functions. Applying those results to mean values of Dirichlet L-functions, we also give an explicit formula for certain mean values of double Dirichlet L-functions.
Kohji Matsumoto, Hirofumi Tsumura (2006)
Acta Arithmetica
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Jörn Steuding (2005)
Acta Mathematica Universitatis Ostraviensis
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We prove explicit upper bounds for the density of universality for Dirichlet series. This complements previous results [15]. Further, we discuss the same topic in the context of discrete universality. As an application we sharpen and generalize an estimate of Reich concerning small values of Dirichlet series on arithmetic progressions in the particular case of the Riemann zeta-function.