• Corpus ID: 252568145

On the Northcott property of Dedekind zeta functions

@inproceedings{Genereux2022OnTN,
  title={On the Northcott property of Dedekind zeta functions},
  author={Xavier G'en'ereux and Matilde Lal'in},
  year={2022}
}
. The Northcott property for special values of Dedekind zeta functions and more general motivic L -functions was defined by Pazuki and Pengo. We investigate this property for any complex evaluation of Dedekind zeta functions. The results are more delicate and subtle than what was proven for the function field case in previous work of Li and the authors, since they include some surprising behavior in the neighborhood of the trivial zeros. The techniques include a mixture of analytic and computer… 
View PDF on arXiv

References

SHOWING 1-10 OF 21 REFERENCES

On the Northcott property of zeta functions over function fields

On the Northcott property for special values of L-functions.

We propose an investigation on the Northcott, Bogomolov and Lehmer properties for special values of $L$-functions. We first introduce an axiomatic approach to these three properties. We then focus on…

Some effective cases of the Brauer-Siegel Theorem

Let k be an algebraic number field of degree n~ and discriminant D~. We let Kk denote the residue of ~(s), " " the zeta function of k, at s = 1. One version of the Brauer-Siegel Theorem is that if k…

Tamely Ramified Towers and Discriminant Bounds for Number Fields

The root discriminant of a number field of degree n is the nth root of the absolute value of its discriminant. Let R2m be the minimal root discriminant for totally complex number fields of degree 2m,…

Some analytic estimates of class numbers and discriminants

This paper presents some new lower bounds (Theorem 1) for the absolute value of the discriminant of a number field. Although not as good for large degrees as some of the author's recent estimates,…

Integral Moments of L‐Functions

We give a new heuristic for all of the main terms in the integral moments of various families of primitive L‐functions. The results agree with previous conjectures for the leading order terms. Our…

Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions : a survey of recent results

2014 A bibliography of recent papers on lower bounds for discriminants of number fields and related topics is presented. Some of the main methods, results, and open problems are discussed.

Multiplicative Number Theory

From the contents: Primes in Arithmetic Progression.- Gauss' Sum.- Cyclotomy.- Primes in Arithmetic Progression: The General Modulus.- Primitive Characters.- Dirichlet's Class Number Formula.- The…

The second moment of quadratic Dirichlet L-functions

On the distribution of extreme values of zeta and $L$-functions in the strip $1/2<\sigma<1$

We study the distribution of large (and small) values of several families of $L$-functions on a line $\text{Re(s)}=\sigma$ where $1/2<\sigma<1$. We consider the Riemann zeta function $\zeta(s)$ in…