Results 41 to 50 of about 71,113 (177)
Some arithmetic properties of partial zeta functions weighted by a sign character
Journal of Number Theory, 2009 AbstractWe introduce two types of zeta functions (Ψ-type and ζ-type) of one complex variable associated to an arbitrary number field K. We prove various arithmetic identities which involve both of them. We also study their special values at integral arguments.
Hugo Chapdelaine
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Spectral zeta functions of fractals and the complex dynamics of polynomials [PDF]
, 2005 We obtain formulas for the spectral zeta function of the Laplacian on symmetric finitely ramified fractals, such as the Sierpinski gasket, and a fractal Laplacian on the interval.
Teplyaev, Alexander
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Values of zeta functions of arithmetic surfaces at $s=1$
, 2021 29 pages; revised version following suggestions of referee; to appear in JIMJ (Journal of the Institute of Mathematics of Jussieu)
Lichtenbaum, Stephen +1 more
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Multiplicity estimate for solutions of extended Ramanujan's system [PDF]
, 2011 We establish a new multiplicity lemma for solutions of a differential system extending Ramanujan's classical differential relations. This result can be useful in the study of arithmetic properties of values of Riemann zeta function at odd positive ...
Zorin, Evgeniy
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Additive Cellular Automata and Volume Growth
Entropy, 2000 : A class of dynamical systems associated to rings of S-integers in rational function fields is described. General results about these systems give a rather complete description of the well-known dynamics in one-dimensional additive cellular automata ...
Thomas B. Ward
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Another generalization of the gcd-sum function [PDF]
, 2013 We investigate an arithmetic function representing a generalization of the gcd-sum function, considered by Kurokawa and Ochiai in 2009 in connection with the multivariable global Igusa zeta function for a finite cyclic group.
Tóth, László
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The fourth moment of the Hurwitz zeta function [PDF]
Journal für die Reine und Angewandte MathematikWe prove a sharp upper bound for the fourth moment of the Hurwitz zeta function ζ ( s , α ) \zeta(s,\alpha) on the critical line when the shift parameter 𝛼 is irrational and of irrationality exponent strictly less than 3. As a consequence, we determine
Winston Heap, Anurag Sahay
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``Quasi''-norm of an arithmetical convolution operator and the order of the Riemann zeta function [PDF]
Functiones et Approximatio Commentarii Mathematici, 2013 In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = ni® for its connection to the Riemann zeta function on the line
Titus Hilberdink
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Igusa’s Local Zeta Functions and Exponential Sums for Arithmetically Non Degenerate Polynomials [PDF]
Journal de Théorie des Nombres de Bordeaux, 2018 We study the twisted local zeta function associated to a polynomial in two variables with coefficients in a non-Archimedean local field of arbitrary characteristic. Under the hypothesis that the polynomial is arithmetically non degenerate, we obtain an explicit list of candidates for the poles in terms of geometric data obtained from a family of ...
Adriana A. Albarracin-Mantilla +1 more
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K3 mirror symmetry, Legendre family and Deligne's conjecture for the Fermat quartic
Nuclear Physics B, 2021 In this paper, we will study the connections between the mirror symmetry of K3 surfaces and the geometry of the Legendre family of elliptic curves. We will prove that the mirror map of the Dwork family is equal to the period map of the Legendre family ...
Wenzhe Yang
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