Results 11 to 20 of about 73,515 (215)

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   +9 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   +6 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   +10 more sources

VALUES OF ZETA FUNCTIONS OF ARITHMETIC SURFACES AT s = 1 [PDF]

Journal of the Institute of Mathematics of Jussieu, 2021
29 pages; revised version following suggestions of referee; to appear in JIMJ (Journal of the Institute of Mathematics of Jussieu)
Stephen Lichtenbaum, Niranjan Ramachandran   +1 more
semanticscholar   +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   +5 more sources

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, Edwin León-Cardenal   +1 more
openalex   +4 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   +3 more sources

Arithmetic expressions of Selberg's zeta functions for congruence subgroups [PDF]

Journal of Number Theory, 2004
12 ...
Yasufumi Hashimoto
openalex   +4 more sources

Zeta Functions on Arithmetic Surfaces [PDF]

, 2013
We use a form of lifted harmonic analysis to develop a two-dimensional adelic integral representation of the zeta functions of simple arithmetic surfaces. Manipulations of this integral then lead to an adelic interpretation of the so-called mean-periodicity correspondence, which is comparable to the better known automorphicity conjectures for the ...
Thomas Oliver
openalex   +3 more sources

The Mean Square of the Hurwitz Zeta-Function in Short Intervals

Axioms
The Hurwitz zeta-function ζ(s,α), s=σ+it, with parameter ...
Antanas Laurinčikas, Darius Šiaučiūnas   +1 more
doaj   +2 more sources