Results 131 to 140 of about 5,312,961 (166)

On the zero-distribution of Epstein zeta-functions

Mathematische Annalen, 2005
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Extreme Values of the Epstein Zeta Functions

Journal of Mathematical Sciences, 2017
From the text: In 1928, \textit{E. C. Titchmarsh} proved the following fact (Titchmarsh's phenomenon, see ``The Theory of the Riemann zeta-function.'' 2nd ed. Oxford: Clarendon Press (1986; Zbl 0601.10026), Theorem 8.12). Let \(\sigma\) be a fixed number, \(1/2\leq \sigma < 1\). Then the inequality \[ |\zeta(\sigma + it)| > \exp(\log^\alpha t) \tag{1} \
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ON EPSTEIN'S ZETA FUNCTION OF HUMBERT FORMS

International Journal of Number Theory, 2008
The Epstein ζ function ζ(Γ,s) of a lattice Γ is defined by a series which converges for any complex number s such that ℜ s > n/2, and admits a meromorphic continuation to the complex plane, with a simple pole at s = n/2. The question as to which Γ, for a fixed s, minimizes ζ(Γ,s), has a long history, dating back to Sobolev's work on numerical ...
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On the zeros of the Epstein zeta functions. II

Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 1998
This continues a study of the behavior of the Epstein zeta-function for a quadratic form with \(8\times 8\) diagonal matrix having 4 ones and 4 \(d\)'s on the diagonal [Part I, cf. J. Math. Kyoto Univ. 36, 697-770 (1996; Zbl 0888.11015)]. Here \(d>0\). It is shown that the \(\sqrt{d}\)-analogue of the Riemann hypothesis holds.
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On the zeros of certain Epstein zeta functions

Forum Mathematicum, 2008
Summary: This paper studies the distribution of zeros of certain Epstein zeta functions, associated to positive definite binary quadratic forms with class number 2, in the region of absolute convergence of their Dirichlet series. In particular, one obtains upper and lower bounds for the rate of approach of zeros to the boundary of the zero-free half ...
Bombieri, Enrico, Mueller, Julia
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On Riesz Means of the Coefficients of Epstein’s Zeta Functions

Journal of Mathematical Sciences, 2018
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Order of the Epstein Zeta-Function in the Critical Strip

Journal of Mathematical Sciences, 2002
Let \(Q(x_1,\dots,x_k)\) be a positive definite quadratic form of \(k\geq 2\) variables, and let \(\zeta(s,Q)\) be its Epstein zeta-function. The growth rate of \(\zeta(s,Q)\) on the line \(\Re s=(k-1)/2\) is investigated. For \(k\geq 4\) and for an integral form \(Q\), the problem is reduced to a similar problem on the behavior of the Dirichlet \(L ...
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Generalized multidimensional Epstein zeta functions

Journal of Mathematical Physics, 1994
Explicit formulas are given for the expression of multiple-sum zeta functions of the type ∑l1,...,lN=−∞∞[a1(l1 − c1)2 +... + aN(lN − cN)2 + M2]−s, where ai≳0, M2≥0, i=1,...,N, in terms of Riemann and Hurwitz zeta functions and in terms of Kelvin functions. Using different analytical continuation methods several formulas, especially useful for different
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On a problem about the Epstein zeta-function

Mathematical Proceedings of the Cambridge Philosophical Society, 1964
1. Letbe a positive definite binary quadratic form with determinant αβ − δ2 = 1. A special form of this kind isWe consider the Epstein zeta-functionthe series converging for . The function Zh(s) can be analytically continued over the whole s-plane and it is regular except for a simple pole with residue π at s = 1.
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On the Laurent series for the Epstein zeta function

Journal of Physics A: Mathematical and Theoretical, 2016
The Epstein zeta function ζ d [ M ; s ] ≡ ∑ n ∈ Z d ' ( n M n T ) − s 2 , where is a real symmetric and invertible d × d matrix and is a d-dimensional row vector with integer coordinates , is considered. (The prime on the sum indicates that the term should be excluded.) It is known that has a Laurent series expansion about the singular point s = d ...
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