1 citations · 1 across the 14 of their papers we have counts for
15 papers
Absolute minimum of a height associated to a semipositive adelic line bundle
Shu Kawaguchi, Fabien Pazuki
There exists a semipositive adelic line bundle on a projective variety over whose absolute minimum does not attain the minimum by algebraic points. The construction is…
Drinfeld modules in rank 2 with CM and S-unit j-invariants
Liam Baker, Fabien Pazuki, Patricio Perez Pina
We prove the finiteness of the set of -invariants of Drinfeld modules of rank 2 over which are CM and -units, for the infinite set of primes with even d…
Infinite extensions with finitely many CM moduli
Shu Kawaguchi, Fabien Pazuki
We show that there are uncountably many algebraic extensions of containing at most finitely many moduli of CM simple principally polarized abelian varieties of any fix…
Distortion maps for elliptic curves over finite fields
Nikita Andrusov, Sevag Büyüksimkeşyan, Dimitrios Noulas +3
The Weil pairing on elliptic curves has deep links with discrete logarithm problems. In practice, to better suit the functionalities of cryptosystems, one often needs to modify the…
A computational approach to Drinfeld modules
Cécile Armana, Elena Berardini, Xavier Caruso +3
This survey provides a practical and algorithmic perspective on Drinfeld modules over . Starting with the construction of the Carlitz module, we present Drinfeld mo…
A parallelogram height inequality for Drinfeld modules
Liam Baker, Richard Griffon, Fabien Pazuki
We prove an inequality relating the Taguchi heights of four Drinfeld modules arranged in a ``parallelogram of isogenies''. This inequality is the analogue for Drinfeld modules of t…
Partitions and Hecke images
Florian Breuer, Fabien Pazuki
We obtain a new family of relations satisfied by the partition function. In contrast with most partition relations, these involve non-trivial roots of unity. We present two proofs,…
Variation of height in an isogeny class over a function field
Richard Griffon, Samuel Le Fourn, Fabien Pazuki
We give optimal estimates on the variation of the differential and modular heights within an isogeny class of abelian varieties defined over the function field of a curve (in any c…
On Diophantine properties for values of Dedekind zeta functions
Jerson Caro, Fabien Pazuki, Riccardo Pengo
We study the Northcott and Bogomolov property for special values of Dedekind -functions at real values . We prove, in particular, that the Bogomolov property is…
Heights of Drinfeld modular polynomials and Hecke images
Florian Breuer, Fabien Pazuki, Zhenlin Ran
We obtain explicit upper and lower bounds on the size of the coefficients of the Drinfeld modular polynomials for any monic . These polynomials vanish at…
Drinfeld singular moduli, hyperbolas, units
Bruno Anglès, Cécile Armana, Vincent Bosser +1
Let be a prime power and consider Drinfeld modules of rank 2 over . We prove that there are no points with coordinates being Drinfeld singular moduli, on…
Explicit bounds on the coefficients of the modular polynomials and the size of
Florian Breuer, Desirée Gijón Gómez, Fabien Pazuki
We give explicit upper and lower bounds on the size of the coefficients of the modular polynomials for the elliptic -function. These bounds make explicit the best previous…
Explicit bounds on the coefficients of modular polynomials for the elliptic -invariant
Florian Breuer, Fabien Pazuki
We obtain an explicit upper bound on the size of the coefficients of the elliptic modular polynomials for any . These polynomials vanish at pairs of -invariants of…
Ordinary isogeny graphs over : the inverse volcano problem
Henry Bambury, Francesco Campagna, Fabien Pazuki
We give a detailed presentation of -isogeny graphs associated with ordinary elliptic curves defined over . We then focus on the following inverse problem: given…
The regulator dominates the rank
Fabien Pazuki
After noticing that the regulator of a number field dominates the rank of its group of units, we bound from below the regulator of the Mordell-Weil group of elliptic curves over gl…