Results 1 to 10 of about 17,305 (155)
The Riemann-zeta function on vertical arithmetic progressions [PDF]
International Mathematics Research Notices, 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
core +7 more sources
Zeta functions of regular arithmetic schemes at s=0 [PDF]
Duke Mathematical Journal, 2013 Lichtenbaum conjectured the existence of a Weil-\'etale cohomology in order to describe the vanishing order and the special value of the Zeta function of an arithmetic scheme $\mathcal{X}$ at $s=0$ in terms of Euler-Poincar\'e characteristics.
Morin, Baptiste
core +7 more sources
Computing zeta functions of arithmetic schemes [PDF]
Proceedings of the London Mathematical Society, 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
core +4 more sources
Well-rounded zeta-function of planar arithmetic lattices [PDF]
Proceedings of the American Mathematical Society, 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
core +7 more sources
Arithmetic expressions of Selberg's zeta functions for congruence subgroups [PDF]
Journal of Number Theory, 2006 In Sarnak's paper, it was proved that the Selberg zeta function for SL(2,Z) is expressed in terms of the fundamental units and the class numbers of the primitive indefinite binary quadratic forms.
Hashimoto, Yasufumi
core +4 more sources
SPECIAL VALUES OF THE ZETA FUNCTION OF AN ARITHMETIC SURFACE [PDF]
Journal of the Institute of Mathematics of Jussieu, 2021 AbstractWe 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 results in the proof.
Matthias Flach, Daniel Siebel
openaire +3 more sources
The Riemann Zeta Function on Arithmetic Progressions [PDF]
Experimental Mathematics, 2012 We prove asymptotic formulas for the first discrete moment of the Riemann zeta function on certain vertical arithmetic progressions inside the critical strip. The results give some heuristic arguments for a stochastic periodicity that we observed in the phase portrait of the zeta function.
Steuding, J örn, Wegert, Elias
openaire +2 more sources
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
core +3 more sources
An arithmetic formula for certain coefficients of the Euler product of Hecke polynomials [PDF]
, 2004 In 1997 the author found a criterion for the Riemann hypothesis for the Riemann zeta function, involving the nonnegativity of certain coefficients associated with the Riemann zeta function. In 1999 Bombieri and Lagarias obtained an arithmetic formula for
Li, Xian-Jin
core +3 more sources
Algebraic independence of arithmetic gamma values and Carlitz zeta values [PDF]
, 2008 We consider the values at proper fractions of the arithmetic gamma function and the values at positive integers of the zeta function for F_q[theta] and provide complete algebraic independence results for them.Comment: 15 ...
Chang, Chieh-Yu +3 more
core +4 more sources