scholarly journals An explicit upper bound for the least prime ideal in the Chebotarev density theorem

2019 ◽  
Vol 69 (3) ◽  
pp. 1411-1458 ◽  
Author(s):  
Jeoung-Hwan Ahn ◽  
Soun-Hi Kwon
Keyword(s):  
Prime Ideal ◽  
Upper Bound ◽  
Density Theorem ◽  
Chebotarev Density Theorem

scholarly journals A bound for the least prime ideal in the Chebotarev Density Theorem

1979 ◽  
Vol 54 (3) ◽  
pp. 271-296 ◽  
Author(s):  
J. C. Lagarias ◽  
H. L. Montgomery ◽  
A. M. Odlyzko
Keyword(s):  
Prime Ideal ◽  
Density Theorem ◽  
Chebotarev Density Theorem

scholarly journals The least prime ideal in the Chebotarev density theorem

2019 ◽  
Vol 147 (6) ◽  
pp. 2289-2303 ◽  
Author(s):  
Habiba Kadiri ◽  
Nathan Ng ◽  
Peng-Jie Wong
Keyword(s):  
Prime Ideal ◽  
Density Theorem ◽  
Chebotarev Density Theorem

scholarly journals An explicit Chebotarev density theorem under GRH

2019 ◽  
Vol 200 ◽  
pp. 441-485 ◽  
Author(s):  
Loïc Grenié ◽  
Giuseppe Molteni
Keyword(s):  
Density Theorem ◽  
Chebotarev Density Theorem

Positive deissler rank and the complexity of injective modules

1988 ◽  
Vol 53 (1) ◽  
pp. 284-293 ◽  
Author(s):  
T. G. Kucera
Keyword(s):  
Prime Ideal ◽  
Lower Bounds ◽  
Upper Bound ◽  
Noetherian Ring ◽  
Krull Dimension ◽  
Primary Ideal ◽  
Prime Ideals ◽  
Commutative Noetherian Ring ◽  
Injective Modules ◽  
Primary Ideals

This is the second of two papers based on Chapter V of the author's Ph.D. thesis [K1]. For acknowledgements please refer to [K3]. In this paper I apply some of the ideas and techniques introduced in [K3] to the study of a very specific example. I obtain an upper bound for the positive Deissler rank of an injective module over a commutative Noetherian ring in terms of Krull dimension. The problem of finding lower bounds is vastly more difficult and is not addressed here, although I make a few comments and a conjecture at the end.For notation, terminology and definitions, I refer the reader to [K3]. I also use material on ideals and injective modules from [N] and [Ma]. Deissler's rank was introduced in [D].For the most part, in this paper all modules are unitary left modules over a commutative Noetherian ring Λ but in §1 I begin with a few useful results on totally transcendental modules and the relation between Deissler's rank rk and rk+.Recall that if P is a prime ideal of Λ, then an ideal I of Λ is P-primary if I ⊂ P, λ ∈ P implies that λn ∈ I for some n and if λµ ∈ I, λ ∉ P, then µ ∈ I. The intersection of finitely many P-primary ideals is again P-primary, and any P-primary ideal can be written as the intersection of finitely many irreducible P-primary ideals since Λ is Noetherian. Every irreducible ideal is P-primary for some prime ideal P. In addition, it will be important to recall that if P and Q are prime ideals, I is P-primary, J is Q-primary, and J ⊃ I, then Q ⊃ P. (All of these results can be found in [N].)

scholarly journals Conditional upper bound for the k-th prime ideal with given Artin symbol

2020 ◽  
Vol 213 ◽  
pp. 271-284
Author(s):  
Loïc Grenié ◽  
Giuseppe Molteni
Keyword(s):  
Prime Ideal ◽  
Upper Bound

scholarly journals Knots which behave like the prime numbers

2013 ◽  
Vol 149 (8) ◽  
pp. 1235-1244 ◽  
Author(s):  
Curtis T. McMullen
Keyword(s):  
Number Fields ◽  
Prime Numbers ◽  
Density Theorem ◽  
Chebotarev Density Theorem

AbstractThis paper establishes a version of the Chebotarev density theorem in which number fields are replaced by 3-manifolds.

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