相关论文: Moments of restricted divisor functions
We derive sharp lower bounds for L^p-functions on the n-dimensional unit hypercube in terms of their p-th marginal moments. Such bounds are the unique solutions of a system of constrained nonlinear integral equations depending on the…
Assuming the generalized Riemann hypothesis, we evaluate sharp upper bounds for the shifted moments of quadratic Dirichlet L-functions with moduli 8p, where p ranges over odd primes. We then apply this result to prove bounds for the moments…
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
This article deals with time-fractional diffusion equations with time-dependent singular source term. Whenever the order of the time-fractional derivative is either multi-term, distributed or space-dependent, we prove that the system admits…
Let $u_n$ be a fixed non-degenerate binary recurrence sequence with positive discriminant, $w$ a fixed non-zero integer and $p_1,p_2,\dots,p_s$ fixed, distinct prime numbers. In this paper we consider the Diophantine equation $u_n+u_m=w…
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
Expressions are given for the truncated fractional moments $E X_+^p$ of a general stable law. These involve families of special functions that arose out of the study of multivariate stable densities and probabilities. As a particular case,…
Optimal approximation and optimal interpolation problems on the classes of periodic functions that are determined by restrictions on several higher derivatives of the functions are solved.
The solution of QCD equations for generating functions of multiplicity distributions reveals new peculiar features of cumulant moments oscillating as functions of their rank. This prediction is supported by experimental data on $e^{+}e^{-},…
Proportional delay is a particular case of time dependent delay. In this article, we consider differential equations involving multiple delays. The series solution of this equation leads to a class of special functions. This class of…
We investigate the properties of the moments of the cot function using the central factorial numbers. Using a new integral representation of the central factorial numbers, we find a new way to express these moments in terms of recursive…
Given a multiplicative function $f$, we let $S(x,f)=\sum_{n\leq x}f(n)$ be the associated partial sum. In this note, we show that lower bounds on partial sums of divisor-bounded functions result in lower bounds on the partial sums…
This paper presents a novel method for analytical derivations of marginal densities using the fractional derivatives of moment-generating functions. Although the method requires likelihood functions to take specific forms, its assumptions…
We show that if one can compute a little more than a particular moment for some family of L-functions, then one has upper bounds of the conjectured order of magnitude for all smaller (positive, real) moments and a one-sided central limit…
The main purpose of this work is to prove characterization theorems for generalized moment functions on groups. According one of the main results these are exponential polynomials that can be described with the aid of complete (exponential)…
We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…
We examine the value distributions of coefficients in certain $q$-series related to half Appell sums in higher-level and the first moment of the Garvan's $k$-rank of partitions. We prove that these coefficients equal certain restricted…
We derive the equations of motion for all the irreducible moments of the single-particle distribution function. We find that these moment equations of motion are highly coupled, with the dynamics of lower-rank moments always being coupled…
Assume a polynomial-time algorithm for factoring integers, Conjecture~\ref{conj}, $d\geq 3,$ and $q$ and $p$ are prime numbers, where $p\leq q^A$ for some $A>0$. We develop a polynomial-time algorithm in $\log(q)$ that lifts every…