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of 5
pro vyhledávání: '"Viglino, Ilaria"'
We prove tight probabilistic bounds for the shortest vectors in module lattices over number fields using the results of arXiv:2308.15275. Moreover, establishing asymptotic formulae for counts of fixed rank matrices with algebraic integer entries and
Externí odkaz:
http://arxiv.org/abs/2402.10305
Autor:
Viglino, Ilaria
For $ f\in\mathbb{Z}[X] $ an irreducible polynomial of degree $ n $, the Cilleruelo's conjecture states that$$\log(\mbox{lcm}(f(1),\dots,f(M)))\sim(n-1)M\log M$$as $ M\rightarrow+\infty $, where $ \mbox{lcm}(f(1),\dots,f(M)) $ is the least common mul
Externí odkaz:
http://arxiv.org/abs/2402.03999
Autor:
Viglino, Ilaria
The van der Waerden's Conjecture states that the set $\mathscr{P}_{n,N}^0(\mathbb{Q})$ of monic integer polynomials $f(X)$ of degree $n$, with height $\le N$ such that the Galois group $G_{K_f/\mathbb{Q}}$ of the splitting field $K_f/\mathbb{Q}$ is t
Externí odkaz:
http://arxiv.org/abs/2212.11608
Autor:
Viglino, Ilaria
We study the distributions of the splitting primes in certain families of number fields. The first and main example is the family Pn,N of integer polynomials monic of degree n with height less or equal then N, and then let N go to infinity. We prove
Externí odkaz:
http://arxiv.org/abs/2212.08103