Related papers: Subconvexity for $\rm{GL}(3)$ L-functions

We give a Burgess-like subconvex bound for $L(s, \pi \otimes \chi)$ in terms of the analytical conductor of $\chi$, where $\pi$ is a $GL_2$ cuspidal representation and $\chi$ is a Hecke character.

In the presence of certain topological conditions, we provide lower bounds for the infimum of the length function associated to a collection of curves on Teichm\"uller space that depend on the dual cube complex associated to the collection,…

The problem of finding upper bounds for L-functions at the edge of the critical strip has a long and interesting history. Here, the situation for classical L-functions such as Dirichlet L-functions is relatively well understood. The reason…

The aim of this short note is to give counterexamples to two results by D. Y. Gao [5, Th. 16], [4, Th. 2] and to improve a related result by S.-C. Fang, D. Y. Gao, R.-L. Sheu and S.-Y. Wu [1, Th. 3].

The main objective of this article is to compute a first moment for product of Dirichlet and twisted self-dual $GL(3)$ $L$-functions. We discuss the possible simultaneous non vanishing at the central point. We use properties of symmetric…

This paper introduces the proper notion of variational quasiconvexity associated to a group of diffeomorphisms. We prove a lower semicontinuity theorem connected to this notion. In the second part of the paper we apply this result to a…

Let $\phi$ be a spherical Hecke-Maass cusp form on the non-compact space $\mathrm{PGL}_3(\mathbb{Z})\backslash\mathrm{PGL}_3(\mathbb{R})$. We establish various pointwise upper bounds for $\phi$ in terms of its Laplace eigenvalue…

We give uniform upper and lower bounds for the L^2 norm of the restriction of eigenfunctions of the Laplacian on the three-dimensional standard flat torus to surfaces with non-vanishing curvature. We also present several related results…

The note provides a description of the homology of $GL_3$ over function rings of affine elliptic curves over arbitrary fields, following the earlier work of Takahashi and Knudson in the case $GL_2$. Some prospects for applications to…

We introduce the the fractional Laplacian on a subgraph of a graph with Dirichlet boundary condition. For a lattice graph, we prove the upper and lower estimates for the sum of the first $k$ Dirichlet eigenvalues of the fractional…

We prove a couple of new endpoint geodesic restriction estimates for eigenfunctions. In the case of general 3-dimensional compact manifolds, after a $TT^*$ argument, simply by using the $L^2$-boundedness of the Hilbert transform on $\R$, we…

This paper studies minimax optimization problems $\min_x \max_y f(x,y)$, where $f(x,y)$ is $m_x$-strongly convex with respect to $x$, $m_y$-strongly concave with respect to $y$ and $(L_x,L_{xy},L_y)$-smooth. Zhang et al. provided the…

A non-symmetric reciprocity formula is established that expresses the fourth moment of automorphic L-functions of level q and primitive central character twisted by the l-th Hecke eigenvalue as a twisted mixed moment of automorphic…

For a fixed SL(3, Z) Maass form g, we consider the family of L-functions L(g \times u_j, s) where u_j runs over the family of Hecke-Maass cusp forms on SL(2,Z). We obtain an estimate for the second moment of this family of L-functions at…

Linear singularly perturbed convection-diffusion problems with characteristic layers are considered in three dimensions. We demonstrate the sharpness of our recently obtained upper bounds for the associated Green's function and its…

Let $f\in S_k(N,\psi)$ be a newform, and let $\chi$ be a primitive character of conductor $q^{\ell}$. Assume that $q$ is a prime and $\ell>1$. In this paper we describe a method to establish convexity breaking bounds of the form $$…

We obtain explicit solutions of the mean curvature flow in some submanifolds of the Euclidean space. We give particularly an explicit solution of the flow of a hypersurface in the Lagrangian self-expander $L$ which is constructed in the…

Let $f$ be a $p$-primitive cusp form of level $p^{4r}$, where local representation of $f$ be supercuspidal at $p$, $p$ being an odd prime, $r\geq 1$ and $g$ be a Hecke-Maass or holomorphic primitive cusp form for…

We investigate the sixth moment of the family of $L$-functions associated to holomorphic modular forms on $GL_2$ with respect to a congruence subgroup $\Gamma_1(q)$. We improve on previous work and obtain an unconditional upper bound of the…

The action for the su(N) SDYM equations is shown to give in the limit $N \to \infty$ the action for the six-dimensional version of the second heavenly equation. The symmetry reductions of this latter equation to the well known equations of…