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pro vyhledávání: '"Grenié, Loïc"'
Let $d$ be any positive and non square integer. We prove an upper bound for the first two moments of the length $T(d)$ of the period of the continued fraction expansion for $\sqrt{d}$. This allows to improve the existing results for the large deviati
Externí odkaz:
http://arxiv.org/abs/2401.13118
Autor:
Grenié, Loïc, Molteni, Giuseppe
Under the assumption of the validity of the Generalized Riemann Hypothesis, we prove that the class group of every field of degree $n$ and discriminant with absolute value $\Delta$ can be generated using prime ideals with norm $\leq (4-1/(2n))\log^2\
Externí odkaz:
http://arxiv.org/abs/2212.09461
For any integer $N \geq 1$, let $\mathfrak{E}_N$ be the set of all Egyptian fractions employing denominators less than or equal to $N$. We give upper and lower bounds for the cardinality of $\mathfrak{E}_N$, proving that $$ \frac{N}{\log N} \prod_{j
Externí odkaz:
http://arxiv.org/abs/1906.11986
Autor:
Grenié, Loïc, Molteni, Giuseppe
We prove an explicit upper bound for the k-th prime ideal with fixed Artin symbol, under the assumption of the validity of the Riemann hypothesis for the Dedekind zeta functions.
Comment: We have improved the introduction and made clearer some c
Comment: We have improved the introduction and made clearer some c
Externí odkaz:
http://arxiv.org/abs/1906.01994
Publikováno v:
Mathematika; Oct2024, Vol. 70 Issue 4, p1-12, 12p
Autor:
Grenié, Loïc, Molteni, Giuseppe
Assuming Generalized Riemann's Hypothesis, Bach proved that the class group $\mathcal C\!\ell_{\mathbf K}$ of a number field ${\mathbf K}$ may be generated using prime ideals whose norm is bounded by $12\log^2\Delta_{\mathbf K}$, and by $(4+o(1))\log
Externí odkaz:
http://arxiv.org/abs/1607.02430
Publikováno v:
International Journal of Number Theory, 2019
We prove explicit versions of Cram\'er's theorem for primes in arithmetic progressions, on the assumption of the generalized Riemann hypothesis.
Comment: A misprint in a formula has been corrected; all constants appearing in the conclusions have
Comment: A misprint in a formula has been corrected; all constants appearing in the conclusions have
Externí odkaz:
http://arxiv.org/abs/1606.08616
Autor:
Grenié, Loïc, Molteni, Giuseppe
We have proved recently several explicit versions of the prime ideal theorem under GRH. Here we prove a version with optimal asymptotic behaviour.
Comment: Followed referee's advice including changing title
Comment: Followed referee's advice including changing title
Externí odkaz:
http://arxiv.org/abs/1602.03515
Autor:
Grenié, Loïc, Molteni, Giuseppe
In [BDyDF08] Belabas, Diaz y Diaz and Friedman show a way to determine, assuming the Generalized Riemann Hypothesis, a set of prime ideals that generate the class group of a number field. Their method is efficient because it produces a set of ideals
Externí odkaz:
http://arxiv.org/abs/1507.00602
On the assumption of the Riemann hypothesis, we give explicit upper bounds on the difference between consecutive prime numbers.
Comment: Corrected Corollary 4.1. Minor changes to the bibliography. To appear in Int. J. Number Theory
Comment: Corrected Corollary 4.1. Minor changes to the bibliography. To appear in Int. J. Number Theory
Externí odkaz:
http://arxiv.org/abs/1503.05403