Related papers: The saddle-point method and the Li coefficients

We consider the semi-classical generalized Freud weight function \[w_{\lambda}(x;t) = |x|^{2\lambda+1}\exp(-x^4 +tx^2),\qquad x\in\mathbb{R},\] with $ \lambda>-1$ and $t\in\mathbb{R}$ parameters. We analyze the asymptotic behavior of the…

We consider a fluid queue where the input process consists of N identical sources that turn on and off at exponential waiting times. The server works at the constant rate c and an on source generates fluid at unit rate. This model was first…

We consider the asymptotic expansion of the generalised exponential integral involving the Mittag-Leffler function introduced recently by Mainardi and Masina [{\it Fract. Calc. Appl. Anal.} {\bf 21} (2018) 1156--1169]. We extend the…

We define a tau function for a generic Riemann-Hilbert problem posed on a union of non-intersecting smooth closed curves with jump matrices analytic in their neighborhood. The tau function depends on parameters of the jumps and is expressed…

We study the leading coefficient in the asymptotical formula $ N (R) = \frac{W}{\pi} R + O (1) $, $ R \to \infty $, for the resonance counting function $ N (R)$ of Schr\"odinger Hamiltonians with point interactions. For such Hamiltonians,…

The analytic properties of automorphic L-functions have historically been obtained either through integral representations (the "Rankin-Selberg method"), or properties of the Fourier expansions of Eisenstein series (the "Langlands-Shahidi…

We introduce the Local Increasing Regularity Method (LIRM) which allows us to get from \emph{local} a priori estimates, on solutions $u$ of a linear equation $\displaystyle Du=\omega ,$ \emph{global} ones. As an application we shall prove…

Motivated by the application of saddlepoint approximations to resampling-based statistical tests, we prove that the Lugannani-Rice formula has vanishing relative error when applied to approximate conditional tail probabilities of averages…

In this paper, we propose a primal-dual algorithm with a novel momentum term using the partial gradients of the coupling function that can be viewed as a generalization of the method proposed by Chambolle and Pock in 2016 to solve saddle…

We propose an inexact Uzawa algorithm with two variable relaxation parameters for solving the generalized saddle-point system. The saddle-point problems can be found in a wide class of applications, such as the augmented Lagrangian…

In this paper we derive non-classical Tauberian asymptotic at infinity for the tail, the density and the derivatives thereof of a large class of exponential functionals of subordinators. More precisely, we consider the case when the L\'evy…

In [Solving second order ordinary differential equations by extending the Prelle-Singer method, J. Phys. A: Math.Gen., 34, 3015-3024 (2001)] we defined a function (we called S) associated to a rational second order ordinary differential…

We consider a bivariate rational generating function F(x,y) = P(x,y) / Q(x,y) = sum_{r, s} a_{r,s} x^r y^s under the assumption that the complex algebraic curve $\sing$ on which $Q$ vanishes is smooth. Formulae for the asymptotics of the…

The generalized Einstein Hilbert action is an extension of the classic scalar curvature energy and Perelman F functional which incorporates a closed three-form. The critical points are known as generalized Ricci solitons, which arise…

We define an S function as the sum of the asymptotic error terms of digamma function of an arithmetic series, $S(a) \equiv \sum_{n=1}^\infty \left[\ln\frac{n}{a} - \frac{a}{2n}-\psi\left(\frac{n}{a}\right)\right]$, and show a few properties…

Let $\{e_j\}$ be an orthonormal basis of Laplace eigenfunctions of a compact Riemannian manifold $(M,g)$. Let $H \subset M$ be a submanifold and let $\{\psi_k\}$ be an orthonormal basis of Laplace eigenfunctions of $H$ with the induced…

In this paper, we consider the $k$-th Riesz mean for the coefficients of the Rankin-Selberg $L$-function $L_{f \times f}(s)$ related to the Godement-Jacquet $L$-function with respect to $SL(n,\mathbb{Z})$. We establish an asymptotic formula…

The transformations of the sum identities for generalized harmonic and oscillatory numbers, obtained earlier in our recent report [1], enable us to derive the new identities expressed in terms of the corresponding square roots of x. At…

Let $d(n)$ be the number of divisors of $n$, let $\gamma$ denote Euler's constant and $$ \Delta(x) := \sum_{n\le x}d(n) - x(\log x + 2\gamma -1) $$ denote the error term in the classical Dirichlet divisor problem, and let $\zeta(s)$ denote…

Fix an elliptic curve $E/\Q$, and assume the generalized Riemann hypothesis for the $L$-function $ L(E_D, s) $ for every quadratic twist $E_D$ of $E$ by $D\in\Z$. We combine Weil's explicit formula with techniques of Heath-Brown to derive…