Related papers: Norm bounds on Eisenstein series

A theory of transversely oriented spun-normal immersed surfaces in ideally triangulated 3--manifolds is developed in this paper, including linear functionals determining the boundary curves, Euler characteristic and homology class of these…

We study elliptic and parabolic systems in divergence form with degenerate or singular coefficients. Under the conormal boundary condition on the flat boundary, we establish boundary Schauder type estimates when the coefficients have…

We develop a method for proving sup-norm and H\"older estimates for $\overline{\partial}$ on wide class of finite type pseudoconvex domains in $\mathbb{C}^n$. A fundamental obstruction to proving sup-norm estimates is the possibility of…

We prove non-trivial bounds for general bilinear forms in hyper-Kloosterman sums when the sizes of both variables may be below the P\'olya-Vinogradov range. We then derive applications to the second moment of holomorphic cusp forms twisted…

In this paper we consider certain classes of generalized double Eisenstein series by simple differential calculations of trigonometric functions. In particular, we give four new transformation formula for some double Eisenstein series. We…

We exhibit the first examples of hyperbolic three-manifolds for which the Seiberg-Witten equations do not admit any irreducible solution. Our approach relies on hyperbolic geometry in an essential way; it combines an explicit upper bound…

Combining $2$-descent techniques with Riemann-Roch and B\'ezout's theorems, we give an upper bound on the number of rational points of bounded height on elliptic and hyperelliptic curves over function fields of characteristic $\neq 2$. We…

We study the quantum limits of Eisenstein series off the critical line for $\mathrm{PSL}_{2}(\mathcal{O}_{K})\backslash\mathbb{H}^{3}$, where $K$ is an imaginary quadratic field of class number one. This generalises the results of Petridis,…

In this paper we review some author's results about Weingarten surfaces in Euclidean space $\r^3$ and hyperbolic space $\h^3$. We stress here in the search of examples of linear Weingarten surfaces that satisfy a certain geometric property.…

In this article using the theory of Eisenstein series, we give rise to the complete evaluation of two Gauss hypergeometric functions. Moreover we evaluate the modulus of each of these functions and the values of the functions in terms of…

In this article, we have studied transformation formulas of zeta function at odd integers over an arbitrary number field which in turn generalizes Ramanujan's identity for the Riemann zeta function. The above transformation leads to a new…

Our main result is that for all sufficiently large $x_0>0$, the set of commensurability classes of arithmetic hyperbolic 2- or 3-orbifolds with fixed invariant trace field $k$ and systole bounded below by $x_0$ has density one within the…

We prove quantitative norm bounds for a family of operators involving impedance boundary conditions on convex, polygonal domains. A robust numerical construction of Helmholtz scattering solutions in variable media via the…

We study the $L^2$ norm of the Eisenstein series $E(z,1/2+iT)$ restricted to a segment of a geodesic connecting infinity and an arbitrary real. We conjecture that on slightly thickened geodesics of this form, the Eisenstein series satifies…

In this article, we consider Einstein-type manifolds with boundary which generalizes important geometric equations, like static vacuum and static perfect fluid. We investigate some geometric inequalities for those manifolds. Then, we…

We consider the problem of finding complete conformal metrics with prescribed curvature functions of the Einstein tensor and of more general modified Schouten tensors. To achieve this, we reveal an algebraic structure of a wide class of…

We identify a class of "semi-modular" forms invariant on special subgroups of $GL_2(\mathbb Z)$, which includes classical modular forms together with complementary classes of functions that are also nice in a specific sense. We define an…

We develop a unified approach to the construction of the hyperbolic and elliptic Eisenstein series on a finite volume hyperbolic Riemann surface. Specifically, we derive expressions for the hyperbolic and elliptic Eisenstein series as…

We prove that the modular symbols appropriately normalized and ordered have an asymptotical normal distribution for all cocompact subgroups of SL_2(R). We introduce hyperbolic Eisenstein series in order to calculate the moments of the…

We study a Neumann type initial-boundary value problem for strongly degenerate parabolic-hyperbolic equations under the nonlinearity-diffusivity condition. We suggest a notion of entropy solution for this problem and prove its uniqueness.…