Results 51 to 60 of about 71,113 (177)

Multiple finite Riemann zeta functions

, 2004
Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then, describe the ...
Kimoto, K., Kurokawa, N., Matsumoto, S., Wakayama, M.   +3 more
core   +1 more source

The Arithmetic Site [PDF]

, 2014
We show that the non-commutative geometric approach to the Riemann zeta function has an algebraic geometric incarnation: the "Arithmetic Site".
Connes, Alain, Consani, Caterina
core   +3 more sources

Generalized Twin Prime Formulas

, 2010
Based on Golomb's arithmetic formulas, Dirichlet series for two classes of twin primes are constructed and related to the roots of the Riemann zeta function in the critical strip.Comment: 17 pages, no ...
Weber, H. J.
core   +1 more source

Modular Calabi-Yau fourfolds and connections to M-theory fluxes

Journal of High Energy Physics
In this work, we study the local zeta functions of Calabi-Yau fourfolds. This is done by developing arithmetic deformation techniques to compute the factor of the zeta function that is attributed to the horizontal four-form cohomology.
Hans Jockers, Sören Kotlewski, Pyry Kuusela   +2 more
doaj   +1 more source

Li coefficients and the quadrilateral zeta function

Canadian mathematical bulletin
In this note, we study the Li coefficients $\lambda _{n,a}$ for the quadrilateral zeta function. Furthermore, we give an arithmetic and asymptotic formula for these coefficients.
Kajtaz H. Bllaca, K. Mazhouda, Takashi Nakamura   +2 more
semanticscholar   +1 more source

A note on the dynamical zeta function of general toral endomorphisms

, 2009
It is well-known that the Artin-Mazur dynamical zeta function of a hyperbolic or quasi-hyperbolic toral automorphism is a rational function, which can be calculated in terms of the eigenvalues of the corresponding integer matrix.
Baake, Michael, Lau, Eike, Paskunas, Vytautas   +2 more
core   +3 more sources

Difference independence of the Riemann zeta function

, 2006
It is proved that the Riemann zeta function does not satisfy any nontrivial algebraic difference equation whose coefficients are meromorphic functions $\phi$ with Nevanlinna characteristic satisfying $T(r, \phi)=o(r)$ as $r\to \infty$Comment: To appear ...
Chiang, Yik-Man, Feng, Shaoji
core   +3 more sources

Geometry of the arithmetic site [PDF]

, 2015
We introduce the Arithmetic Site: an algebraic geometric space deeply related to the non-commutative geometric approach to the Riemann Hypothesis. We prove that the non-commutative space quotient of the adele class space of the field of rational numbers ...
Connes, Alain, Consani, Caterina
core  

Motivic Serre invariants, ramification, and the analytic Milnor fiber

, 2007
We show how formal and rigid geometry can be used in the theory of complex singularities, and in particular in the study of the Milnor fibration and the motivic zeta function.
A. Bravo, A. Grothendieck, A. Grothendieck, A. Grothendieck, A.J. Jong de, B. Conrad, B. Rodrigues, D. Eisenbud, F. Loeser, G. Guibert, G. Kempf, J. Denef, J. Denef, J. Igusa, J. Milnor, J. Nicaise, J. Sebag, Johannes Nicaise, Julien Sebag, L. Illusie, N. A’Campo, N. A’Campo, P. Deligne, S. Bosch, S. Bosch, S. Bosch, S. Bosch, V. Kulikov, V.G. Berkovich, V.G. Berkovich   +29 more
core   +2 more sources

Poincaré series of Lie lattices and representation zeta functions of arithmetic groups

, 2017
We compute explicit formulae for Dirichlet generating functions enumerating finite-dimensional irreducible complex representations of potent and saturable principal congruence subgroups of $\mathrm{SL}_4^m(\mathfrak{o})$ ($m\in\mathbb{N}$) for $\mathfrak{o}$ a compact DVR of characteristic $0$ and odd residue field characteristic.
Michele Zordan
openalex   +4 more sources