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In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex…
A 1976 result from Norton may be used to give an asymptotic (but not explicit) description of the constant in Mertens' second theorem for primes in arithmetic progressions. Assuming the Generalized Riemann Hypothesis, we give an effective…
This working paper describes new results in derivations of the Continuous Ranked Probability Score of a generalized beta-prime distribution and several special cases, such as the Dagum distribution and Singh-Maddala distribution. Comparison…
We investigate the distribution of $p\theta$ modulo 1, where $\theta$ is a complex number which is not contained in $\mathbb{Q}(i)$, and $p$ runs over the Gaussian primes.
Assuming that the Generalized Riemann Hypothesis (GRH) holds, we prove an explicit formula for the number of representations of an integer as a sum of $k\geq 5$ primes. Our error terms in such a formula improve by some logarithmic factors…
We propose a generalization of the Elliott-Halberstam conjecture concerning the distribution of prime pairs in arithmetic progressions. This conjecture, which we call the Generalized Elliott-Halberstam Conjecture for Shifted Convolutions…
An expression for the joint probability distribution of the principal curvatures at an arbitrary point in the ensemble of isosurfaces defined on isotropic Gaussian random fields on Rn is derived. The result is obtained by deriving symmetry…
Building on the concept of pretentious multiplicative functions, we give a new and largely elementary proof of the best result known on the counting function of primes in arithmetic progressions.
We introduce a complex q-Fourier transform as a generalization of the (real) one analyzed in [Milan J. Math. {\bf 76} (2008) 307]. By recourse to tempered ultradistributions we show that this complex plane-generalization overcomes all…
It is well-known that the equations for a simple fluid can be cast into what is called their Lagrange formulation. We introduce a notion of a generalized Lagrange formulation, which is applicable to a wide variety of systems of partial…
Representations of primes by simple quadratic forms, such as $\pm a^2\pm qb^2$, is a subject that goes back to Fermat, Lagrange, Legendre, Euler, Gauss and many others. We are interested in a comprehensive list of such results, for $q\le…
Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized…
We present in this work a heuristic expression for the density of prime numbers. Our expression leads to results which possesses approximately the same precision of the Riemann's function in the domain that goes from 2 to 1010 at least.…
The prime number problem falls within the realm of number theory, specifically elementary number theory. Current research approaches have unnecessarily complicated this matter. In contrast to more advanced mathematical tools, the methods of…
If the prime numbers are pseudo-randomly distributed, then analogy with quantum systems suggests that counting primes might be modeled by a non-homogeneous Poisson process. Consequently, postulating underlying gamma statistics, more-or-less…
We show that the Generalized Sato-Tate Conjecture permits to obtain rather precise information on the distribution of the consecutive quadratic residues modulo large primes.
We present a systematic study of galaxy biasing in the presence of primordial non-Gaussianity. For a large class of non-Gaussian initial conditions, we define a general bias expansion and prove that it is closed under renormalization,…
In this work, we extend the definition of the graded prime ideals from those in commutative graded rings to the ideals over graded Lie algebras. We prove some facts about graded prime Lie ideals in arbitrary Lie algebras that are similar to…
We study the distribution of primes from a topological viewpoint. Certain conjecture is introduced, and we show that it is equivalent to the Riemann Hypothesis.
The central limit theorem provides the theoretical foundation for the universality of the normal distribution: under broad conditions, the asymptotic distribution of a sum of independent random variables approaches a Gaussian. Yet, physical…