3,435 research outputs found
Multiple finite Riemann zeta functions
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
-series identity for proving the zeta function has an Euler product and
then, describe the location of zeros. We study further multi-variable and
multi-parameter versions of the multiple finite Riemann zeta functions and
their infinite counterparts in connection with symmetric polynomials and some
arithmetic quantities called powerful numbers.Comment: 19 page
Observation of Bell Inequality violation in B mesons
A pair of mesons from decay exhibit EPR type
non-local particle-antiparticle (flavor) correlation. It is possible to write
down Bell Inequality (in the CHSH form: ) to test the non-locality
assumption of EPR. Using semileptonic decays of at Belle
experiment, a clear violation of Bell Inequality in particle-antiparticle
correlation is observed:
S=2.725+-0.167(stat)+-0.092(syst)Comment: Conference Proceeding for Garda Lake Workshop 2003 "Mysteries,
Puzzles and Paradoxes in Quantum Mechanics
On a conjecture by Boyd
The aim of this note is to prove the Mahler measure identity
which was conjectured by
Boyd. The proof is achieved by proving relationships between regulators of both
curves
Congruence schemes
A new category of algebro-geometric objects is defined. This construction is
a vast generalization of existing F1-theories, as it contains the the theory of
monoid schemes on the one hand and classical algebraic theory, e.g.
Grothendieck schemes, on the the other. It also gives a handy description of
Berkovich subdomains and thus contains Berkovich's approach to abstract
skeletons. Further it complements the theory of monoid schemes in view of
number theoretic applications as congruence schemes encode number theoretical
information as opposed to combinatorial data which are seen by monoid schemes
Hierarchy of the Selberg zeta functions
We introduce a Selberg type zeta function of two variables which interpolates
several higher Selberg zeta functions. The analytic continuation, the
functional equation and the determinant expression of this function via the
Laplacian on a Riemann surface are obtained.Comment: 14 page
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