REVIEW 2 cited by
Power Savings for Counting (Twisted) Abelian Extensions of Number Fields
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
We prove significant power savings for the error term when counting abelian extensions of number fields (as well as the twisted version of these results for nontrivial Galois modules). In some cases over $\mathbb{Q}$, these results reveal lower order terms following the same structure as the main term that were not previously known. Assuming the generalized Lindel\"of hypothesis for Hecke $L$-functions, we prove square root power savings for the error compared to the order of the main term.
Forward citations
Cited by 2 Pith papers
-
Inductive methods for counting number fields
Introduces a fiber-summation inductive method that proves new cases of Malle's conjecture and gives counterexamples to Malle's predicted exponents for wreath products.
-
An Explicit Tauberian Theorem taking Averaged Inputs with an Application to Counting Abelian Number Fields
An explicit Tauberian theorem using twisted moment bounds instead of pointwise bounds yields square-root-saving error terms for counting C_n-extensions of Q for n = 3, 4, 8, 16, and 2p.
Discussion (0). Continue with ORCID to comment.