Assuming the Riemann hypothesis, we prove estimates for variance of real and imaginary part logarithm zeta function in short intervals. We give three different formulations these results. a conjecture Chan how often gaps between zeros can be close to fixed non-zero value, Berry (1988) number non-universal regime. In this range, Gaussian unitary ensemble statistics do not describe distribution z...

We study the real x–zeros of the derivative C ν (x) of the cylinder function Cν(x) = Cν(x, α) = cosαJν(x) − sinαYν(x) for ν < 0. For fixed α, 0 ≤ α < π and n = 1, 2, . . ., we show the existence of a number νn in the interval −n+ α/π − 1 < ν < −n+ α/π such that the first positive zero of C ν (x) occurs after the first positive zero of Cν(x) when −n− 1 + α/π < ν < νn and before the first positiv...

BackgroundCount data represents the number of occurrences an event within a fixed period time. In count modelling, overdispersion is inevitable. Sometimes, this may not be just due to excess zeros but presence two or more mixtures. Hence main objective examine for mixtures if any, with and compare Generalized Poisson model, Mixture models other using real time simulated data.MethodsThree over-d...

Abstract: The probability that a random polynomial of degree n with i.i.d exponentially distributed coefficients has all real zeros is P(All zeros are real) = E ∏ 1≤j<k≤n |Uj − Uk| = ( n−1 ∏

We discuss asymptotics of the zeros of orthogonal polynomials on the real line and on the unit circle when the recursion coefficients are periodic. The zeros on or near the absolutely continuous spectrum have a clock structure with spacings inverse to the density of zeros. Zeros away from the a.c. spectrum have limit points mod p and only finitely many of them.