Related papers: A Subconvex Metaplectic Prime Geodesic Theorem and…

Let $(M,g)$ be a two-dimensional compact boundaryless Riemannian manifold with nonpostive curvature, then we shall give improved estimates for the $L^2$-norms of the restrictions of eigenfunctions to unit-length geodesics, compared to the…

The sub-optimality of Gauss--Hermite quadrature and the optimality of the trapezoidal rule are proved in the weighted Sobolev spaces of square integrable functions of order $\alpha$, where the optimality is in the sense of worst-case error.…

This paper investigates enumerative aspects of permutohedral blades, which provide a generalization of the notion of the tropical hyperplane arrangement. Blade provide the combinatorial underpinning of generalized biadjoint scalar…

In this paper, we establish the multiplicative ergodic theorem for McKean-Vlasov stochastic differential equations, in which the Lyapunov exponent is defined using the upper limit. The reasonability of this definition is illustrated through…

We discuss two generalizations of the collar lemma. The first is the stable neighborhood theorem which says that a (not necessarily simple) closed geodesic in a hyperbolic surface has a \lq\lq stable neighborhood\rq\rq whose width only…

In this paper we analyse the well-posedness of the Cauchy problem for a rather general class of hyperbolic systems with space-time dependent coefficients and with multiple characteristics of variable multiplicity. First, we establish a…

A method to compute guaranteed lower bounds to the eigenvalues of the Maxwell system in two or three space dimensions is proposed as a generalization of the method of Liu and Oishi [SIAM J. Numer. Anal., 51, 2013] for the Laplace operator.…

This work introduces an unconventional inexact augmented Lagrangian method where the augmenting term is a Euclidean norm raised to a power between one and two. The proposed algorithm is applicable to a broad class of constrained nonconvex…

We establish quantitative strengthenings of Mazur's conjecture regarding the non-torsion property of higher Heegner points on modular and Shimura curves, confirming both a vertical version for sufficiently large powers $n$ and a horizontal…

For $\Gamma$ a cocompact or cofinite Fuchsian group, we study the hyperbolic lattice point problem in conjugacy classes, which is a modification of the classical hyperbolic lattice point problem. We use large sieve inequalities for the…

Let $\Gamma$ be a cocompact discrete subgroup of $\mathrm{PSL}_{2}(\mathbb{C})$ and denote by $\mathcal{H}$ the three dimensional upper half-space. For a $p\in\mathcal{H}$, we count the number of points in the orbit $\Gamma p$, according to…

We give here a new proof of a Tauberian Theorem of complex Laplace transform using the Theory of measure and theory of function with bounded variations. However we deduce the simple proof of Prime Number Theorem.

In our previous paper [SIMAX 31 n.3 1491-1506(2010)], we studied the condition metric in the space of maximal rank matrices. Here, we show that this condition metric induces a Lipschitz-Riemann structure on that space. After investigating…

In this paper, we consider the problem of improving 2D triangle meshes tessellating planar regions. We propose a new variational principle for improving 2D triangle meshes where the energy functional is a convex function over the angle…

A classical open problem in combinatorial geometry is to obtain tight asymptotic bounds on the maximum number of k-level vertices in an arrangement of n hyperplanes in d dimensions (vertices with exactly k of the hyperplanes passing below…

Interior-point methods (IPMs) are a cornerstone of Euclidean convex optimization, due to their strong theoretical guarantees and practical performance. Motivated by scaling problems, recent work by Hirai and the last two authors (FOCS'23)…

In this paper, we analyze the simplex method with the largest distance rule and derive upper bounds on the number of different basic feasible solutions generated. The pivoting rule was proposed by Pan [10], and in some cases, it was…

A central problem in discrete geometry, known as Hadwiger's covering problem, asks what the smallest natural number $N\left(n\right)$ is such that every convex body in ${\mathbb R}^{n}$ can be covered by a union of the interiors of at most…

We show a Prime Geodesic Theorem for the group SL3(Z), counting those geodesics whose lifts lie in the split Cartan subgroup. This is the first arithmetic Prime Geodesic Theorem of higher rank for a non-cocompact group.

For sets $A, B\subset \mathbb N$, their sumset is $A + B := \{a+b: a\in A, b\in B\}$. If we cannot write a set $C$ as $C = A+B$ with $|A|, |B|\geq 2$, then we say that $C$ is $\textit{irreducible}$. The question of whether a given set $C$…