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We improve the error term in the asymptotic formula for the twisted fourth moment of automorphic L functions of prime level and weight two proved by Kowalski, Michel and Vanderkam. As a consequence, we obtain a new subconvexity bound in the…

Number Theory · Mathematics 2016-02-29 Olga Balkanova , Dmitry Frolenkov

Assuming the Riemann hypothesis, we establish an upper bound for the $2k$-th discrete moment of the derivative of the Riemann zeta-function at nontrivial zeros, where $k$ is a positive real number. Our upper bound agrees with conjectures of…

Number Theory · Mathematics 2020-04-28 Scott Kirila

A new bound for the remainder term in the Taylor expansion of the complex exponent $e^{ix}$, $x\in\R$, is proved yielding precise moment-type estimates of the accuracy of the approximation of the characteristic function (the…

Probability · Mathematics 2018-04-02 Irina Shevtsova

We study the general moment problem for measures on the real line, with polynomials replaced by more general spaces of entire functions. As a particular case, we describe measures that are uniquely determined by a restriction of their…

Classical Analysis and ODEs · Mathematics 2014-06-03 Mishko Mitkovski , Alexei Poltoratski

We prove near-optimal upper bounds for the odd moments of the distribution of coprime residues in short intervals, confirming a conjecture of Montgomery and Vaughan. As an application we prove near-optimal upper bounds for the average of…

Number Theory · Mathematics 2026-05-13 Thomas F. Bloom , Vivian Kuperberg

We prove convergence with optimal algebraic rates for an adaptive finite element method for nonlinear equations with strongly monotone operator. Unlike prior works, our analysis also includes the iterative and inexact solution of the…

Numerical Analysis · Mathematics 2018-11-27 Gregor Gantner , Alexander Haberl , Dirk Praetorius , Bernhard Stiftner

In this paper we use techniques first introduced by Florea to improve the asymptotic formula for the first moment of the quadratic Dirichlet L-functions over the rational function field, running over all monic, square-free polynomials of…

Number Theory · Mathematics 2019-08-13 J. C. Andrade , J. MacMillan

We consider the long time behavior of Wong-Zakai approximations of stochastic differential equations. These piecewise smooth diffusion approximations are of great importance in many areas, such as those with ordinary differential equations…

Probability · Mathematics 2023-10-10 Pierre Del Moral , Shulan Hu , Ajay Jasra , Hamza Ruzayqat , Xinyu Wang

In this paper, we have proved four theorems on the degree of approximation of continuous functions by matrix means of their Fourier series which is expressed in terms of the modulus of continuity and a non-negative mediate function.

Classical Analysis and ODEs · Mathematics 2023-06-22 Xhevat Z. Krasniqi

We estimate asymptotically the fourth moment of the Riemann zeta-function twisted by a Dirichlet polynomial of length $T^{\frac14 - \varepsilon}$. Our work relies crucially on Watt's theorem on averages of Kloosterman fractions. In the…

Number Theory · Mathematics 2016-09-09 Sandro Bettin , H. M. Bui , Xiannan Li , Maksym Radziwiłł

We construct a general procedure for the Quasi Likelihood Analysis applied to a multivariate point process on the real half line in an ergodic framework. More precisely, we assume that the stochastic intensity of the underlying model…

Statistics Theory · Mathematics 2016-09-28 Simon Clinet , Nakahiro Yoshida

We establish the validity of the empirical Edgeworth expansion (EE) for a studentized trimmed mean, under the sole condition that the underlying distribution function of the observations satisfies a local smoothness condition near the two…

Statistics Theory · Mathematics 2011-06-28 Nadezhda Gribkova , Roelof Helmers

We prove exact formulas for weighted $2k$th moments of the Riemann zeta function for all integer $k\geq 1$ in terms of the analytic continuation of an auto-correlation function. This latter enjoys several functional equations. One of them,…

Number Theory · Mathematics 2023-11-07 Sébastien Darses , Joseph Najnudel

In this paper, we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights, these processes can exhibit long-range…

Statistics Theory · Mathematics 2011-03-21 Jérôme Dedecker , Florence Merlevède , Magda Peligrad

We establish a central limit theorem for a class of pre-averaging covariance estimators in a general endogenous time setting. In particular, we show that the time endogeneity has no impact on the asymptotic distribution if certain…

Statistics Theory · Mathematics 2015-10-21 Yuta Koike

Recently, it was observed that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In particular, under mild assumptions on the…

Classical Analysis and ODEs · Mathematics 2015-05-22 James Bremer , Vladimir Rokhlin

We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…

Astrophysics · Physics 2007-05-23 Luca Amendola

We study the asymptotic behaviour of different statistics for time series exhibiting long memory and nonstationarity. For processes with memory parameter $d\in(-1/2,3/2)$, we derive the joint limiting distribution of discrete Fourier…

Statistics Theory · Mathematics 2026-05-28 Mohamedou Ould Haye , Anne Philippe

We compute the deterministic approximation for mixed fluctuation moments of products of deterministic matrices and general Sobolev functions of Wigner matrices. Restricting to polynomials, our formulas reproduce recent results of [Male,…

Probability · Mathematics 2024-09-19 Jana Reker

The minimax theory for estimating linear functionals is extended to the case of a finite union of convex parameter spaces. Upper and lower bounds for the minimax risk can still be described in terms of a modulus of continuity. However in…

Statistics Theory · Mathematics 2007-06-13 T. Tony Cai , Mark G. Low