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math.NT2025
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…
math.AG2025
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…
math.NT2025
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…