Summation formulae and their relation to Dirichlet's series
W. L. Ferrar (1935)
Compositio Mathematica
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W. L. Ferrar (1935)
Compositio Mathematica
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Carletti, E., Bragadin, G.Monti (1993)
International Journal of Mathematics and Mathematical Sciences
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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.
Ben Lichtin (1988)
Compositio Mathematica
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Abou-Tair, Ibrahim A. (1987)
International Journal of Mathematics and Mathematical Sciences
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G. Molteni (2010)
Acta Arithmetica
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G. Molteni (2010)
Acta Arithmetica
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Kohji Matsumoto, Hirofumi Tsumura (2006)
Acta Arithmetica
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A. Mouze (2007)
Annales Polonici Mathematici
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We study universal Dirichlet series with respect to overconvergence, which are absolutely convergent in the right half of the complex plane. In particular we obtain estimates on the growth of their coefficients. We can then compare several classes of universal Dirichlet series.
Zuzana Bukovská (1990)
Mathematica Slovaca
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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.