Untitled

Puchta, J.-C.

doi:10.1023/a:1006711604010

Search citation statements

Order By: Relevance

Paper Sections

Select...

Results Without the Linear Independence Hypothesis2

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2004

2023

Publication Types

Select...

Article4

Other1

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 6 publications

(2 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The following calculation is similar to that of Schlage- Puchta [2000], who computed the moments of e t =2 .e t I /.…”

Section: Results Without the Linear Independence Hypothesismentioning

confidence: 93%

See 1 more Smart Citation

Untitled

2014

Algebra Number Theory

View full text Add to dashboard Cite

show abstract

“…The following calculation is similar to that of Schlage- Puchta [2000], who computed the moments of e t =2 .e t I /.…”

Section: Results Without the Linear Independence Hypothesismentioning

confidence: 93%

“…The calculation of the variance follows from Lemma 2.1 and from Parseval's identity for B 2 almost-periodic functions [Besicovitch 1926]. (An alternative way to compute the variance is to argue as in [Schlage- Puchta 2000]. )…”

Section: Results Without the Linear Independence Hypothesismentioning

confidence: 99%

Untitled

2014

Algebra Number Theory

View full text Add to dashboard Cite

show abstract

Distribution of Frobenius Elements in Families of Galois Extensions

Fiorilli¹,

Jouve

2023

J. Inst. Math. Jussieu

View full text Add to dashboard Cite

Given a Galois extension $L/K$ of number fields, we describe fine distribution properties of Frobenius elements via invariants from representations of finite Galois groups and ramification theory. We exhibit explicit families of extensions in which we evaluate these invariants and deduce a detailed understanding and a precise description of the possible asymmetries. We establish a general bound on the generic fluctuations of the error term in the Chebotarev density theorem, which under GRH is sharper than the Murty–Murty–Saradha and Bellaïche refinements of the Lagarias–Odlyzko and Serre bounds, and which we believe is best possible (assuming simplicity, it is of the quality of Montgomery’s conjecture on primes in arithmetic progressions). Under GRH and a hypothesis on the multiplicities of zeros up to a certain height, we show that in certain families, these fluctuations are dominated by a constant lower order term. As an application of our ideas, we refine and generalize results of K. Murty and of Bellaïche, and we answer a question of Ng. In particular, in the case where $L/{\mathbb {Q}}$ is Galois and supersolvable, we prove a strong form of a conjecture of K. Murty on the unramified prime ideal of least norm in a given Frobenius set. The tools we use include the Rubinstein–Sarnak machinery based on limiting distributions and a blend of algebraic, analytic, representation theoretic, probabilistic and combinatorial techniques.

show abstract

Sign changes of π (x,q,1) - π(x,q,a)

Schlage‐Puchta¹

2004

Acta Mathematica Hungarica

View full text Add to dashboard Cite

Untitled

Cited by 6 publications

References 9 publications

Untitled

Untitled

Distribution of Frobenius Elements in Families of Galois Extensions

Sign changes of π (x,q,1) - π(x,q,a)

Contact Info

Product

Resources

About