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We provide new explicit examples of lattice sphere packings in dimensions 54, 55, 162, 163, 486 and 487 that are the densest known so far, using Kummer families of elliptic curves over global function fields.In some cases, these families of elliptic curves ...
We define p-adic BPS or pBPS invariants for moduli spaces M-beta,M-chi of one-dimensional sheaves on del Pezzo and K3 surfaces by means of integration over a non-archimedean local field F. Our definition relies on a canonical measure mu can on the F-analyt ...
A dual-shot technique based on the field basis addition of two statistically independent speckle patterns is developed to recover an input polarization through a scattering layer. It is proposed theoretically, and demonstrated both numerically and experime ...
In this article, we propose a dynamical system to avoid obstacles which are star shaped and simultaneously converge to a goal. The convergence is almost-global in a domain and the stationary points are identified explicitly. Our approach is based on the id ...
We examine the moments of the number of lattice points in a fixed ball of volume V for lattices in Euclidean space which are modules over the ring of integers of a number field K. In particular, denoting by ωK the number of roots of unity in K, we ...
In this thesis we consider the problem of estimating the correlation of Hecke eigenvalues of GL2 automorphic forms with a class of functions of algebraic origin defined over finite fields called trace functions. The class of trace functions is vast and inc ...
Health requirements for lighting in buildings are becoming increasingly important in building standards. Yet, there is a lack of concrete data on the lighting conditions that prevail in our workplaces, in terms of their spectral characteristics, their seas ...
Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...
In this text, we will show the existence of lattice packings in a family of dimensions by employing division algebras. This construction is a generalization of Venkatesh's lattice packing result Venkatesh (Int Math Res Notices 2013(7): 1628-1642, 2013). In ...
The problem of learning graphons has attracted considerable attention across several scientific communities, with significant progress over the re-cent years in sparser regimes. Yet, the current techniques still require diverg-ing degrees in order to succe ...