An effective Chebotarev density theorem for families of number fields, with an application to -torsion in class groups
LB Pierce, CL Turnage-Butterbaugh… - Inventiones mathematicae, 2020 - Springer
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 …
allows one to count small primes (even as small as an arbitrarily small power of the …
On ℓ-torsion in class groups of number fields
For each integer ℓ≥ 1, we prove an unconditional upper bound on the size of the ℓ-torsion
subgroup of the class group, which holds for all but a zero-density set of field extensions of ℚ …
subgroup of the class group, which holds for all but a zero-density set of field extensions of ℚ …
Bounds for moments of -torsion in class groups
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 …
unconditional upper bounds on the r th moment of ℓ-torsion in the ideal class groups of …
Counting problems: class groups, primes, and number fields
LB Pierce - Proc. Int. Cong. Math, 2022 - ems.press
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 …
certain properties of arithmetic within the ring of integers of the field. The class group is well …
On a conjecture for -torsion in class groups of number fields: from the perspective of moments
LB Pierce, CL Turnage-Butterbaugh… - arXiv preprint arXiv …, 2019 - arxiv.org
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 …
the $\ell $-torsion subgroup is very small (in an appropriate sense, relative to the …
Inductive methods for counting number fields
B Alberts, RJL Oliver, J Wang, MM Wood - arXiv preprint arXiv:2501.18574, 2025 - arxiv.org
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 …
discriminant, which we employ to prove many new cases of Malle's Conjecture and …
Averages and higher moments for the -torsion in class groups
C Frei, M Widmer - Mathematische Annalen, 2021 - Springer
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 …
group of K, as K runs through certain natural families of number fields and ℓ ℓ is a positive …
Bounds for the ‐torsion in class groups
M Widmer - Bulletin of the London Mathematical Society, 2018 - Wiley Online Library
We prove for each integer ℓ⩾ 1 an unconditional upper bound for the size of the ℓ‐torsion
subgroup C l K [ℓ] of the class group of K, which holds for all but a zero density set of number …
subgroup C l K [ℓ] of the class group of K, which holds for all but a zero density set of number …
-torsion and integral points on quartic surfaces
arXiv:2403.13359v1 [math.NT] 20 Mar 2024 Page 1 6-TORSION AND INTEGRAL POINTS ON
QUARTIC SURFACES S. CHAN, P. KOYMANS, C. PAGANO, AND E. SOFOS Abstract. We prove …
QUARTIC SURFACES S. CHAN, P. KOYMANS, C. PAGANO, AND E. SOFOS Abstract. We prove …
-torsion in class groups of certain families of -quartic fields
C An - Journal de théorie des nombres de Bordeaux, 2020 - numdam.org
-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> …
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> …