Effective version of self-approximation for the Riemann zeta function
Sign Up to like & getrecommendations! Published in 2017 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201400107
Abstract: In the paper we prove an effective version of self-approximation for the Riemann zeta function. read more here.
Keywords: approximation riemann; zeta function; effective version; version self ... See more keywords
On discrete universality of the Riemann zeta-function with respect to uniformly distributed shifts
Sign Up to like & getrecommendations! Published in 2017 at "Archiv der Mathematik"
DOI: 10.1007/s00013-016-0998-8
Abstract: The Voronin universality theorem asserts that a wide class of analytic functions can be approximated by shifts $$\zeta (s+i\tau )$$ζ(s+iτ), $$\tau \in \mathbb {R}$$τ∈R, of the Riemann zeta-function. In the paper, we obtain a universality… read more here.
Keywords: zeta function; uniformly distributed; universality; riemann zeta ... See more keywords
On Discrete Universality of the Hurwitz Zeta-Function
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DOI: 10.1007/s00025-017-0702-8
Abstract: In the paper, discrete universality theorems for the Hurwitz zeta-function $$\zeta (s,\alpha )$$ζ(s,α) on the approximation of a wide class of analytic functions by shifts $$\zeta (s+i\varphi (k),\alpha )$$ζ(s+iφ(k),α), where the sequence $$\{\varphi (k)\}$${φ(k)} is… read more here.
Keywords: zeta function; hurwitz zeta; zeta; discrete universality ... See more keywords
Remainder Padé Approximants for the Hurwitz Zeta Function
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DOI: 10.1007/s00025-019-0976-0
Abstract: Following our earlier research, we use the method introduced by the author in Prévost (J Comput Appl Math 67(2):219–235, 1996) named Remainder Padé Approximant in Prévost (Constr Approx 25(1):109–123, 2007), to construct approximations of the Hurwitz zeta… read more here.
Keywords: zeta function; hurwitz zeta; approximants hurwitz; remainder pad ... See more keywords
On the location of the zero-free half-plane of a random Epstein zeta function
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DOI: 10.1007/s00208-017-1589-0
Abstract: In this note we study, for a random lattice L of large dimension n, the supremum of the real parts of the zeros of the Epstein zeta function $$E_n(L,s)$$En(L,s) and prove that this random variable… read more here.
Keywords: zeta function; epstein zeta; half plane; random ... See more keywords
Zeros of the Selberg zeta function for symmetric infinite area hyperbolic surfaces
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DOI: 10.1007/s10711-018-0386-6
Abstract: In the present paper we give a simple mathematical foundation for describing the zeros of the Selberg zeta functions $$Z_X$$ZX for certain very symmetric infinite area surfaces X. For definiteness, we consider the case of three funneled… read more here.
Keywords: zeta function; zeros selberg; symmetric infinite; infinite area ... See more keywords
Computing Extremely Large Values of the Riemann Zeta Function
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DOI: 10.1007/s10723-017-9416-0
Abstract: The paper summarizes the computation results pursuing peak values of the Riemann zeta function. The computing method is based on the RS-Peak algorithm by which we are able to solve simultaneous Diophantine approximation problems efficiently.… read more here.
Keywords: zeta function; function computing; computing extremely; riemann zeta ... See more keywords
On the Poincaré expansion of the Hurwitz zeta function
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DOI: 10.1007/s10986-021-09527-8
Abstract: In this paper, we extend the result of Paris [R.B. Paris, The Stokes phenomenon associated with the Hurwitz zeta function ζ(s, a), Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 461(2053):297–304, 2005] on… read more here.
Keywords: zeta function; hurwitz zeta; expansion;
Higher moment of coefficients of Dedekind zeta function
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DOI: 10.1007/s11464-020-0816-2
Abstract: Let K 3 be a non-normal cubic extension over ℚ:We study the higher moment of the coefficients $${a_{{K_3}}}(n)$$ of Dedekind zeta function over sum of two squares $$\sum\nolimits_{n_1^2 + n_2^2 \leqslant x} {a_{{K_3}}^l(n_1^2 + n_2^2)}… read more here.
Keywords: zeta function; moment coefficients; dedekind zeta; higher moment ... See more keywords
On extended Hurwitz–Lerch zeta function
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DOI: 10.1016/j.jmaa.2016.11.046
Abstract: Abstract This paper investigates an extended form of a beta function B p , q ( x , y ) . We first study the convergence problem of the function B p , q (… read more here.
Keywords: zeta function; hurwitz lerch; extended hurwitz; lerch zeta ... See more keywords
Pair correlation of zeros of the real and imaginary parts of the Riemann zeta-function
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DOI: 10.1016/j.jnt.2017.10.024
Abstract: Abstract We show that if the Riemann Hypothesis is true for the Riemann zeta-function, ζ ( s ) , and 0 a 1 / 2 , then all but a finite number of the zeros… read more here.
Keywords: zeta function; pair correlation; correlation zeros; riemann zeta ... See more keywords