相关论文: Moments of restricted divisor functions
We establish sharp upper bounds on shifted moments of quadratic Dirichlet $L$-functions over function fields. As an application, we prove some bounds for moments of quadratic Dirichlet character sums over function fields.
We prove that for a large class of multiplicative functions, referred to as generalized divisor functions, it is possible to find a lower bound for the corresponding variance in arithmetic progressions. As a main corollary, we deduce such a…
Our paper is devoted to several problems from the field of modified divisors: namely exponential and infinitary divisors. We study the behaviour of modified divisors, sum-of-divisors and totient functions. Main results concern with the…
We study a weighted divisor function $\mathop{{\sum}'}\limits_{mn\leq x}\cos(2\pi m\theta_1)\sin(2\pi n\theta_2)$, where $\theta_i (0<\theta_i<1)$ is a rational number. By connecting it with the divisor problem with congruence conditions,…
We present an analytic method for computing the moments of a sum of independent and identically distributed random variables. The limiting behavior of these sums is very important to statistical theory, and the moment expressions that we…
In experiment, the multiplicity distributions of inelastic processes are truncated due to finite energy, insufficient statistics or special choice of events. It is shown that the moments of such truncated multiplicity distributions possess…
We consider moments of higher powers of quadratic Dirichlet character sums. In a restricted region, we give their asymptotic behavior by using de la Bret\`{e}che's multivariable Tauberian theorem. We also give the lower bound of the…
We consider additive functionals of Markov processes in continuous time with general (metric) state spaces. We derive concentration bounds for their exponential moments and moments of finite order. Applications include diffusions,…
The first part of this paper is devoted to an analysis of moment problems in R^n with supports contained in a closed set defined by finitely many polynomial inequalities. The second part of the paper uses the representation results of…
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…
We investigate the moment and the distribution of $L(1,\x_P),$ where $\x_P$ varies over quadratic characters associated to irreducible polynomials $P$ of degree $2g+1$ over $\mathbb{F}_q[T]$ as $g\to\infty$. In the first part of the paper…
We compute the second moment in the family of quadratic Dirichlet $L$-functions with prime conductors over $\mathbb{F}_q[x]$ when the degree of the discriminant goes to infinity, obtaining one of the lower order terms. We also obtain an…
We consider sequences of additive functionals of difference approximations for uniformly non-degenerate multidimensional diffusions. The conditions are given, sufficient for such a sequence to converge weakly to a W-functional of the…
We present the first numerical investigation of the method proposed in Ref. [1] to utilize gradient flow to obtain precise determinations of higher moments of PDFs from lattice QCD, circumventing power divergent mixing with lower…
From a known result of diophantine equations of the first degree with 2 unknowns we simply find the results of the distribution function of the sequences of positive integers generated by the functions at the origin of the 3x+1 and 5x+1…
We use the circle method to obtain tight bounds on the $L^p$ norm of an exponential sum involving the divisor function for $p > 2$.
We investigate the number of integer solutions to a multiplicative Diophantine approximation problem and show that the associated counting function converges in distribution to a normal law. Our approach relies on the analysis of…
The problem of iterated partial summations is solved for some discrete distributions defined on discrete supports. The power method, usually used as a computational approach to finding matrix eigenvalues and eigenvectors, is in some cases…
We prove a strong simultaneous Diophantine approximation theorem for values of additive and multiplicative functions provided that the functions have certain regularity on the primes.
In this talk we reexamine the possibility of evaluating parton distribution functions from lattice simulations. We show that, while in principle individual moments can be extracted from lattice data, in all cases the process of…