4 citations · 6 across the 13 of their papers we have counts for
16 papers
On the coefficients of the asymptotic of analytic torsion
Mounir Hajli
In this article, we study the asymptotic expansion of the analytic torsion associated with positive Hermitian line bundles on projective spaces. We show that the expansion contains…
General Stirling-Ramanujan Constants are exponential periods and applications
Mounir Hajli, Ricardo Perez-Marco
For , Stirling-Ramanujan constants are the Ramanujan summation of the divergent series . These constants are exponential periods over the e…
Arithmetic theta invariants and arithmetic equilibrium measures
Mounir Hajli
We introduce two new arithmetic invariants associated with Hermitian line bundles on arithmetic varieties, which play the role of the Bergman distortion function in the arithmetic…
Regularized Products over arithmetic Schemes
Mounir Hajli
In this paper, we study the closed points of arithmetic schemes. We accomplish this by showing that the product of the cardinals of residue fields of closed points in an arithmetic…
On the geometry of punctual Hilbert schemes on singular curves and their motivic zeta functions
Mounir Hajli, Hussein Mourtada, Wenhao Zhu
Inspired by the work of Soma and Watari, we define a tree structure on certain subsemimodules of the semigroup associated with an irreducible plane curve singularity . B…
Theta invariants and Lattice-Point Counting in Normed -Modules
Mounir Hajli
Euclidean lattices occupy a central position in number theory, the geometry of numbers, and modern cryptography. In the present article, the theory of Euclidean lattices is employe…
Toward a generalization of Lehmer's problem to adelic curves
Mounir Hajli
In this short note, we investigate the generalization of Lehmer's problem to finitely generated fields over .
On the regularized products of some Dirichlet series
Mounir Hajli
In this paper, we show that the regularized determinants of some Dirichlet series are multiplicative. As an application, we give generalizations of Lerch's formula for the classica…
The arithmetic volume of hypersurfaces in toric varieties and Mahler measures
Mounir Hajli
In this paper we determine the canonical arithmetic volume of hypersurfaces in smooth projective toric varieties. As a consequence, we prove a generalized Hodge index theorem on hy…
The theta invariants and the volume function on arithmetic varieties
Mounir Hajli
We introduce a new arithmetic invariant for hermitian line bundles on an arithmetic variety. We use this invariant to measure the variation of the volume function with respect to t…
Growth of balls of holomorphic sections on projective toric varieties
Mounir Hajli
Let be an equivariant line bundle which is big and nef on a complex projective nonsingular toric variety . Given a continuous toric metric on $\math…
On the zeta functions on the projective complex spaces
Mounir Hajli
In this article, we study the zeta function associated to the Laplace operator acting on the space of the smooth -forms with on the complex projec…
On the normalized arithmetic Hilbert function
Mounir Hajli
Let be a subvariety of dimension n of the projective space over , and the normalized arithmetic Hilbert function of introduced by Phi…
On an arithmetic inequality on
Mounir Hajli
We establish an inequality comparing the height and the -arithmetic volume of toric metrized divisors on . This gives a partial answer to a question o…
On the invariant spectrum on
Mounir Hajli
Motivated by the work of Abreu and Freitas, we study the invariant spectrum of the Laplace operator associated to hermitian line bundles endowed with invariant metrics over $\mathb…
The spectral theory of generalized Laplacians associated to integrable metrics on compact Riemann surfaces
Mounir Hajli
We extend the spectral theory of generalized Laplacians to integrable metrics on compact Riemann surfaces. As a consequence, we attach in a direct way, a holomorphic analytic torsi…