Results 1 to 10 of about 71,063 (160)
Well-rounded zeta-function of planar arithmetic lattices [PDF]
, 2012 We investigate the properties of the zeta-function of well-rounded sublattices of a fixed arithmetic lattice in the plane. In particular, we show that this function has abscissa of convergence at $s=1$ with a real pole of order 2, improving upon a recent
Fukshansky, Lenny
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The Riemann-zeta function on vertical arithmetic progressions [PDF]
, 2012 We show that the twisted second moments of the Riemann zeta function averaged over the arithmetic progression $1/2 + i(an + b)$ with $a > 0$, $b$ real, exhibits a remarkable correspondance with the analogous continuous average and derive several ...
Li, Xiannan, Radziwill, Maksym
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On Discrete Approximation of Analytic Functions by Shifts of the Lerch Zeta Function
Mathematics, 2022 The Lerch zeta function is defined by a Dirichlet series depending on two fixed parameters. In the paper, we consider the approximation of analytic functions by discrete shifts of the Lerch zeta function, and we prove that, for arbitrary parameters and a
Audronė Rimkevičienė +1 more
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VALUES OF ZETA FUNCTIONS OF ARITHMETIC SURFACES AT [PDF]
Journal of the Institute of Mathematics of Jussieu, 2022 We show that the conjecture of [27] for the special value at $s=1$ of the zeta function of an arithmetic surface is equivalent to the Birch–Swinnerton–Dyer conjecture for the Jacobian of the generic fibre.
Stephen Lichtenbaum +1 more
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SPECIAL VALUES OF THE ZETA FUNCTION OF AN ARITHMETIC SURFACE [PDF]
Journal of the Institute of Mathematics of Jussieu, 2021 We prove that the special-value conjecture for the zeta function of a proper, regular, flat arithmetic surface formulated in [6] at $s=1$ is equivalent to the Birch and Swinnerton-Dyer conjecture for the Jacobian of the generic fibre. There are two key
Matthias Flach, Daniel Siebel
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Zeta-regularization of arithmetic sequences [PDF]
EPJ Web of Conferences, 2020 Is it possible to give a reasonable value to the infinite product 1 × 2 × 3 × · · · × n × · · · ? In other words, can we define some sort of convergence of the finite product 1 × 2 × 3 × · · · × n when n goes to infinity?
Allouche Jean-Paul
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Riemann zeta function and arithmetic progression of higher order [PDF]
, 2020 Riemann zeta function has a great importance in number theory, constituting one of the most studied functions. The zeta function, being a series, has a close relationship with the arithmetic progressions (AP).
Hamilton Brito +2 more
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WSEAS Transactions on Mathematics, 2020 In this work we are interested by cotangent sum related to Estermann zeta function in rational arguments. In the first place we look at the maximum and the moment as they did H. Maier and M. Th.
Mouloud Goubi
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Weighted discrete universality of the Riemann zeta-function
Mathematical Modelling and Analysis, 2020 It is well known that the Riemann zeta-function is universal in the Voronin sense, i.e., its shifts ζ(s + iτ), τ ∈ R, approximate a wide class of analytic functions. The universality of ζ(s) is called discrete if τ take values from a certain discrete set.
Antanas Laurinčikas +2 more
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Computing zeta functions of arithmetic schemes [PDF]
, 2015 We present new algorithms for computing zeta functions of algebraic varieties over finite fields. In particular, let X be an arithmetic scheme (scheme of finite type over Z), and for a prime p let zeta_{X_p}(s) be the local factor of its zeta function ...
Harvey, David
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