Zobrazeno 1 - 10
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pro vyhledávání: '"Jones, Nathan P."'
Gravity-driven infiltration of liquid water into unsaturated porous media can be a spatially heterogeneous process due to the gravity fingering instability. When such infiltration occurs in a subfreezing porous medium, liquid water can readily freeze
Externí odkaz:
http://arxiv.org/abs/2407.21197
We undertake the study of profinite quandles. We provide several constructions of profinite quandles from profinite groups, and from other profinite quandle. We characterize which subquandles of profinite quandles are again profinite. Finally, we pro
Externí odkaz:
http://arxiv.org/abs/2406.15387
Assessing instruction quality is a fundamental component of any improvement efforts in the education system. However, traditional manual assessments are expensive, subjective, and heavily dependent on observers' expertise and idiosyncratic factors, p
Externí odkaz:
http://arxiv.org/abs/2404.02444
Under GRH, any element in the multiplicative group of a number field $K$ that is globally primitive (i.e., not a perfect power in $K^*$) is a primitive root modulo a set of primes of $K$ of positive density. For elliptic curves $E/K$ that are known t
Externí odkaz:
http://arxiv.org/abs/2304.03964
Autor:
Jones, Nathan
Consider the elliptic curve $E$ given by the Weierstrass equation $y^2 = x^3 - 11x - 14$, which has complex multiplication by the order of conductor $2$ inside $\mathbb{Z}[i]$. It was recently observed in a paper of Daniels and Lozano-Robledo that, f
Externí odkaz:
http://arxiv.org/abs/2301.01680
Autor:
Jones, Nathan, Lee, Sung Min
Let $E$ be an elliptic curve defined over $\mathbb{Q}$ and, for a prime $p$ of good reduction for $E$ let $\tilde{E}_p$ denote the reduction of $E$ modulo $p$. Inspired by an elliptic curve analogue of Artin's primitive root conjecture posed by S. La
Externí odkaz:
http://arxiv.org/abs/2206.00872
Autor:
Jones, Nathan, Vissuet, Kevin
Let $E$ be an elliptic curve defined over $\mathbb{Q}$. In 1976, Lang and Trotter conjectured an asymptotic formula for the number $\pi_{E,r}(X)$ of primes $p \leq X$ of good reduction for which the Frobenius trace at $p$ associated to $E$ is equal t
Externí odkaz:
http://arxiv.org/abs/2108.08727
Autor:
Jones, Nathan, McMurdy, Ken
We consider the problem of classifying quadruples $(K,E,m_1,m_2)$ where $K$ is a number field, $E$ is an elliptic curve defined over $K$ and $(m_1,m_2)$ is a pair of relatively prime positive integers for which the intersection $K(E[m_1]) \cap K(E[m_
Externí odkaz:
http://arxiv.org/abs/2008.09087
Inspired by the work of Lang-Trotter on the densities of primes with fixed Frobenius traces for elliptic curves defined over $\mathbb{Q}$ and by the subsequent generalization of Cojocaru-Davis-Silverberg-Stange to generic abelian varieties, we study
Externí odkaz:
http://arxiv.org/abs/2006.11269
Autor:
Cojocaru, Alina Carmen, Jones, Nathan
Let $k$ be a global field, let $A$ be a Dedekind domain with $\text{Quot}(A) = k$, and let $K$ be a finitely generated field. Using a unified approach for both elliptic curves and Drinfeld modules $M$ defined over $K$ and having a trivial endomorphis
Externí odkaz:
http://arxiv.org/abs/2002.08411