It is fundamental in number theory to calculate lower bounds for height functions. Grizzard
studied lower bounds for the Weil height in a relative setting. Vidaux and Videla introduced …

On a conjecture of G. Rémond Page 1 Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XV (2016),
599-608 On a conjecture of G. Rémond FRANCESCO AMOROSO Abstract. We provide an …

Let $ p $ be an odd prime and $ L/K $ a $ p $-adic Lie extension whose Galois group is of
the form $\mathbb {Z} _p^{d-1}\rtimes\mathbb {Z} _p $. Under certain assumptions on the …

We answer the question of Vidaux and Videla about the distribution of the Northcott numbers
for the Weil height. We solve the same problem for the weighted Weil heights. These heights …

Let p ≥ 3 p≥ 3 be a prime number. In this article, we study the canonical expansion of the
primitive p^ n pn-th root of unity ζ _ p^ n ζ pn in p-adic Mal'cev–Neumann field L _p L p for n …

Given a Galois extension is Galois and supersolvable, we prove a strong form of a
conjecture of K. Murty on the unramified prime ideal of least norm in a given Frobenius set …

Résumé Récemment, Rémond a énoncé une conjecture très générale pour la minoration
d'une hauteur canonique sur une variété abélienne ou sur une puissance du groupe …

In this paper we find lower bounds on higher moments of the error term in the Chebotarev
density theorem. Inspired by the work of Bella\''{\i} che, we consider general class functions …

Let $ p $ be an odd prime and $ F_ {\infty,\infty} $ a $ p $-adic Lie extension of a number
field $ F $ with Galois group isomorphic to $\mathbb {Z} _p^ r\rtimes\mathbb {Z} _p $, $ r\geq …

Let $ a $ be an integer which is not of the form $ n^ 2$ or $-3 n^ 2$ for $ n\in\mathbb {Z} $.
Let $ E_a $ be the elliptic curve with rational $3 $-isogeny defined by $ E_a: y^ 2= x^ 3+ a …