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We discuss different applications and potentials of reciprocal bianisotropic metasurfaces including uniform and gradient metasurfaces, in particular, with anisotropic, chiral, and omega properties. Based on an analytic analysis, we discuss…
This paper investigates the randomness properties of a function of the divisor pairs of a natural number. This function, the antecedents of which go to very ancient times, has randomness properties that can find applications in…
Telegraphic notes on the historical bibliography of the Gamma function and Eulerian integrals. Correction to some classical references. Some topics of the interest of the author. We provide some extensive (but not exhaustive) bibliography.…
This paper deals with products of moderate-size primes, familiarly known as smooth numbers. Smooth numbers play a crucial role in information theory, signal processing and cryptography. We present various properties of smooth numbers…
Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and…
In this letter we introduce the problem of secrecy reversibility. This asks when two honest parties can distill secret bits from some tripartite distribution $p_{XYZ}$ and transform secret bits back into $p_{XYZ}$ at equal rates using local…
We give an overview of the intimate connections between natural direct and inverse spectral problems for fractal strings, on the one hand, and the Riemann zeta function and the Riemann hypothesis, on the other hand (in joint works of the…
We study the Ruelle zeta function at zero for negatively curved oriented surfaces with boundary. At zero, the zeta function has a zero and its multiplicity is shown to be determined by the Euler characteristic of the surface. This is shown…
Correlations of the type discussed by EPR in their original 1935 paradox for continuous variables exist for the quadrature phase amplitudes of two spatially separated fields. These correlations were experimentally reported in 1992. We…
This paper studies the interplay between probability, number theory, and geometry in the context of relatively prime integers in the ring of integers of a number field. In particular, probabilistic ideas are coupled together with integer…
The prime number 357686312646216567629137 is notable because of the unusual property that it remains prime successively on removing the left digit until there are no remaining digits. We explore here the distributions of the number of left…
Some integral identities involving the Riemann zeta function and functions reciprocal in a kernel involving the Bessel functions $J_{z}(x), Y_{z}(x)$ and $K_{z}(x)$ are studied. Interesting special cases of these identities are derived, one…
Let p and r be two primes and n, m be two distinct divisors of pr. Consider the n-th and m-th cyclotomic polynomials. In this paper, we present lower and upper bounds for the coefficients of the inverse of one of them modulo the other one.…
A review of some recent advances in zeta function techniques is given, in problems of pure mathematical nature but also as applied to the computation of quantum vacuum fluctuations in different field theories, and specially with a view to…
Branched covering Riemann surfaces $(\mathbb{C},f)$ are studied, where $f$ is the Euler Gamma function and the Riemann Zeta function. For both of them fundamental domains are found and the group of covering transformations is revealed. In…
In order to study signed Eulerian numbers, we introduce permutations of a particular type, called parity-alternate permutations, because they take even and odd entries alternately. The objective of this paper is twofold. The first is to…
This article considers the error term of the primes counting function. It applies some recent results on the densities of prime numbers in short intervals to derive an improvement of the error term from subexponential size to fractional…
We prove a reciprocity relation for the twisted second moment of the Riemann Zeta function. This provides an analogue to a formula of Conrey for Dirichlet L-functions
In this paper, we present some applications of a difference equation of degree k in Cryptography and Coding Theory.
A classical theorem of Kempner states that the sum of the reciprocals of positive integers with missing decimal digits converges. This result is extended to much larger families of "missing digits" sets of positive integers with both…