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math.NT2025
Divisibility criteria and coefficient formulas for cyclotomic polynomials
Laura De Carli, Maurizio Laporta
We establish necessary and sufficient conditions for a polynomial to be divisible by a cyclotomic polynomials and derive new formulas involving Ramanujan sums as an application of…
math.NT2025
On the Sierpinski triangle and its generalizations
L. De Carli, A. Echezabal, I. Morell
By examining arithmetic operations between decimal numbers in a given base m we uncover fractal structures that generalize the Sierpinski triangle
math.FA2025
Methods of construction of exponential bases on planar domains
Oleg Asipchuk, Laura De Carli
In this paper, we survey and refine several results -- some previously established in the literature -- that facilitate the construction of exponential bases on planar domains with…