Mean value theorems for the double zeta-function
نویسندگان
چکیده
منابع مشابه
Some Mean Value Theorems for the Riemann Zeta-function and Dirichlet L-functions
The theory of the Riemann zeta-function ζ(s) and Dirichlet L-functions L(s, χ) abounds with unsolved problems. Chronologically the first of these, now known as the Riemann Hypothesis (RH), originated from Riemann’s remark that it is very probable that all non-trivial zeros of ζ(s) lie on the line < s = 12 . Later on Piltz conjectured the same for all of the functions L(s, χ) (GRH). The vertical...
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© Université Bordeaux 1, 1996, tous droits réservés. L’accès aux archives de la revue « Journal de Théorie des Nombres de Bordeaux » (http://jtnb.cedram.org/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier do...
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We derive several mean value formulae on manifolds, generalizing the classical one for harmonic functions on Euclidean spaces as well as the results of Schoen-Yau, Michael-Simon, etc, on curved Riemannian manifolds. For the heat equation a mean value theorem with respect to ‘heat spheres’ is proved for heat equation with respect to evolving Riemannian metrics via a space-time consideration. Som...
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Let x, e > 0, uo < ... u O be real numbers. Let f be a real valued function and let A (h; u, w)f (x) h-d be a difference quotient associated with a generalized Riemann derivative. Set I = (x + uoh, x + Ud+eh) and let f have its ordinary (d 1)st derivative continuous on the closure of I and its dth ordinary derivative f('I) existent on 1. A necessary and sufficient condition that a ...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 2015
ISSN: 0025-5645
DOI: 10.2969/jmsj/06710383