Dirichlet Finite Biharmonic Functions with Dirichlet Finite Laplacians.
Mitsuru Nakai, Leo Sario (1971)
Mathematische Zeitschrift
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Displaying similar documents to “On the Mean Value of Dirichlet Series.”
Dirichlet Finite Biharmonic Functions with Dirichlet Finite Laplacians.
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The joint universality and the generalized strong recurrence for Dirichlet L-functions
Takashi Nakamura (2009)
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On Certain Dirichlet Series Whose Coefficients Are Related to Class Numbers.
Peter L. Walker (1982)
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A Joint Universality Theorem for Dirichlet L-Functions.
Bhaskar Bagchi (1982)
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Asymptotic expansions of the mean values of Dirichlet L-functions.
Masanori Katsurada, Kohji Matsumoto (1991)
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A representation formula for the Dirichlet integral.
Lennart Carleson (1960)
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A Dirichlet Series Associated to Eisenstein Series of Degree Two.
Erik Lippa (1974)
Mathematische Zeitschrift
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On various mean values of Dirichlet L-functions
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.
Trace Properties of the Dirichlet Laplacian.
E.B. Davies (1984/85)
Mathematische Zeitschrift
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Some identities involving the Dirichlet L-function
Zhefeng Xu, Wenpeng Zhang (2007)
Acta Arithmetica
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A note on the fourth moment of Dirichlet L-functions
H. M. Bui, D. R. Heath-Brown (2010)
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The product of two Dirichlet series
Frédéric Bayart (2004)
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Generalized multiple Dirichlet series and generalized multiple polylogarithms
Kohji Matsumoto, Hirofumi Tsumura (2006)
Acta Arithmetica
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Horizontal monotonicity of the modulus of the zeta function, L-functions, and related functions
Yu. Matiyasevich, F. Saidak, P. Zvengrowski (2014)
Acta Arithmetica
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As usual, let s = σ + it. For any fixed value of t with |t| ≥ 8 and for σ < 0, we show that |ζ(s)| is strictly decreasing in σ, with the same result also holding for the related functions ξ of Riemann and η of Euler. The following inequality related to the monotonicity of all three functions is proved: ℜ (η'(s)/η(s)) < ℜ (ζ'(s)/ζ(s)) < ℜ (ξ'(s)/ξ(s)). It is also shown that extending the above monotonicity result for |ζ(s)|, |ξ(s)|, or |η(s)|...