19 citations · 50 across the 17 of their papers we have counts for
20 papers
Procounting measures and the Bateman--Horn conjecture
Luca Demangos, Ignazio Longhi, Francesco Maria Saettone
Let be the ring of -integers in a global field and its profinite completion. We propose a profinite version of the Bateman--Horn conjecture over and provid…
The algebra and applications to Iwasawa theory
Andrea Bandini, Ignazio Longhi
Let and be distinct primes, and let $\G$ be an abelian pro--group. We study the structure of the algebra $Ł:=\Z_\ell[[\G]]$ and of -modules. The algebra turns…
Heights and transcendence of --adic continued fractions
Ignazio Longhi, Nadir Murru, Francesco Maria Saettone
Special kinds of continued fractions have been proved to converge to transcendental real numbers by means of the celebrated Subspace Theorem. In this paper we study the analogous $…
Coset topologies on and arithmetic applications
Ignazio Longhi, Yunzhu Mu, Francesco Maria Saettone
We provide a construction which covers as special cases many of the topologies on integers one can find in the literature. Moreover, our analysis of the Golomb and Kirch topologies…
Densities on Dedekind domains, completions and Haar measure
Luca Demangos, Ignazio Longhi
Let be the ring of -integers in a global field and its profinite completion. We discuss the relation between density in and the Haar measure of : in p…
On the -invariants of abelian varieties over function fields of positive characteristic
King-Fai Lai, Ignazio Longhi, Takashi Suzuki +2
Let be an abelian variety over a global function field of characteristic . We study the -invariant appearing in the Iwasawa theory of over the unramified $\mathbb…