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Displaying 21 – 35 of 35

The mean value of |L(k,χ)|² at positive rational integers k ≥ 1

Stéphane Louboutin (2001)

Colloquium Mathematicae

Let k ≥ 1 denote any positive rational integer. We give formulae for the sums $S_{o d d} (k, f) = \sum_{χ (- 1) = - 1} | L (k, χ) | ²$ (where χ ranges over the ϕ(f)/2 odd Dirichlet characters modulo f > 2) whenever k ≥ 1 is odd, and for the sums $S_{e v e n} (k, f) = \sum_{χ (- 1) = + 1} | L (k, χ) | ²$ (where χ ranges over the ϕ(f)/2 even Dirichlet characters modulo f>2) whenever k ≥ 1 is even.

The Mellin transform of powers of the zeta-function

Aleksandar Ivić, Matti Jutila, Yoichi Motohashi (2000)

Acta Arithmetica

The moments of infinite series.

Ka-Lam Kueh (1988)

Journal für die reine und angewandte Mathematik

The multiplicative and functional independence of Dedekind zeta functions of abelian fields

Roman Marszałek (2005)

Colloquium Mathematicae

It is shown that the multiplicative independence of Dedekind zeta functions of abelian fields is equivalent to their functional independence. We also give all the possible multiplicative dependence relations for any set of Dedekind zeta functions of abelian fields.

The number-theoretic work of Paul Turán

G. Halász (1980)

Acta Arithmetica

The phase transition of the number-theoretical spin chain.

Andreas Knauf, Pierluigi Contucci (1997)

Forum mathematicum

The quickest proof of the prime number theorem

J. Littlewood (1971)

Acta Arithmetica

The Riemann Zeta function and coin tossing.

P.D.T.A. Elliott (1972)

Journal für die reine und angewandte Mathematik

The Spectral Mean Square of Hecke L-functions on the Critical Line

M. Jutila (2004)

Publications de l'Institut Mathématique

The universality of quadratic L-series for prime discriminants

Hidehiko Mishou, Hirofumi Nagoshi (2006)

Acta Arithmetica

The χ-part of the Analytic Class Number Formula, for Global Function Fields

Stéphane Viguié (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

Let F/k be a finite abelian extension of global function fields, totally split at a distinguished place ∞ of k. We show that a complex Gras conjecture holds for Stark units, and we derive a refined analytic class number formula.

Three open problems and a conjecture

Huizeng Qin, Ovidiu Furdui (2015)

Open Mathematics

In this paper we solve three open problems and a conjecture related to the calculations of some classes of multiple series posed by Furdui in [1].

Truncated Infinitesimal Shifts, Spectral Operators and Quantized Universality of the Riemann Zeta Function

Hafedh Herichi, Michel L. Lapidus (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

We survey some of the universality properties of the Riemann zeta function $ζ (s)$ and then explain how to obtain a natural quantization of Voronin’s universality theorem (and of its various extensions). Our work builds on the theory of complex fractal dimensions for fractal strings developed by the second author and M. van Frankenhuijsen in [60]. It also makes an essential use of the functional analytic framework developed by the authors in [25] for rigorously studying the spectral operator $𝔞$ (mapping...

Twists of Hecke L-functions.

David E. ROHRLICH (1992)

Forum mathematicum

Two complete and minimal systems associated with the zeros of the Riemann zeta function

Jean-François Burnol (2004)

Journal de Théorie des Nombres de Bordeaux

We link together three themes which had remained separated so far: the Hilbert space properties of the Riemann zeros, the “dual Poisson formula” of Duffin-Weinberger (also named by us co-Poisson formula), and the “Sonine spaces” of entire functions defined and studied by de Branges. We determine in which (extended) Sonine spaces the zeros define a complete, or minimal, system. We obtain some general results dealing with the distribution of the zeros of the de-Branges-Sonine entire functions. We...

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