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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 inequalities relating the Taguchi heights, respectively the graded heights, of four Drinfeld modules arranged in a ``parallelogram of isogenies''. This inequality is the a…
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,…