We prove a new effective Chebotarev density theorem for Galois extensions L/QL/Q that
allows one to count small primes (even as small as an arbitrarily small power of the …

We describe the relations among the $\ell $-torsion conjecture, a conjecture of Malle giving
an upper bound for the number of extensions, and the discriminant multiplicity conjecture …

Fix a number field k, integers ℓ, n≥ 2, and a prime p. For all r≥ 1, we prove strong
unconditional upper bounds on the r th moment of ℓ-torsion in the ideal class groups of …

Each number field has an associated finite abelian group, the class group, that records
certain properties of arithmetic within the ring of integers of the field. The class group is well …

Elementary abelian groups are finite groups in the form of A=(ℤ/p⁢ ℤ) r for a prime number
p. For every integer ℓ> 1 and r> 1, we prove a non-trivial upper bound on the ℓ-torsion in …

It is conjectured that within the class group of any number field, for every integer $\ell\geq 1$,
the $\ell $-torsion subgroup is very small (in an appropriate sense, relative to the …

We prove upper bounds for the average size of the ℓ ℓ-torsion\, Cl\, _K ℓ Cl K ℓ of the class
group of K, as K runs through certain natural families of number fields and ℓ ℓ is a positive …

We study the distribution of extensions of a number field k with fixed abelian Galois group G,
from which a given finite set of elements of k are norms. In particular, we show the existence …

We give a new method for counting extensions of a number field asymptotically by
discriminant, which we employ to prove many new cases of Malle's Conjecture and …

-torsion in class groups of certain families of D4-quartic fields Page 1 Chen AN l-torsion in
class groups of certain families of D4-quartic fields Tome 32, no 1 (2020), p. 1-23. <http://jtnb.centre-mersenne.org/item?id=JTNB_2020__32_1_1_0> …