H. Kadiri

activity

20042026

most citedUne region explicite sans zero pour la fonction Zeta de Riemann

26 citations · 60 across the 17 of their papers we have counts for

collaborators

19 papers

math.NT2026

Explicit Exponential Sum Estimates and Approximate Functional Equations for the Zeta Function

Natasha Dhiman, Habiba Kadiri, Emily Quesada-Herrera

We show an explicit version of the Van der Corput truncated Poisson summation formula (B-process). By using refined explicit exponential sum estimates, this improves the error term…

math.NT2026

Bounds for Mertens Sums

Samuel Broadbent, Andrew Fiori, Habiba Kadiri +2

In this article we provide new bounds for the Mertens sums and products including $\sum_{p \leq x} p^{- 1}$ and $\prod_{p \leq x} (1 - \frac{1}{p})$ which provide superior exponential a…

math.NT2025

An effective version of Chebotarev's density theorem

Sourabhashis Das, Habiba Kadiri, Nathan Ng

Chebotarev's density theorem asserts that the prime ideals are equidistributed among the conjugacy classes of the Galois group of any normal extension of number fields. An effectiv…

math.NT2024★ 1 cited

Comparative Prime Number Theory Problem List

Alia Hamieh, Habiba Kadiri, Greg Martin +1

This is a list of problems that were collected from participants at the Comparative Prime Number Theory Symposium held at UBC from June 17 to June 21, 2024. Its goal is to stimulat…

math.NT2024

Moments of $L$ -functions Problem List

Alia Hamieh, Habiba Kadiri, Nathan Ng +1

This is an ongoing list of problems that has resulted from the PIMS (Pacific Institute of Mathematical Sciences) Collaborative Research Group L-functions in Analytic Number Theory:…

math.NT2022

Sharper bounds for the error term in the Prime Number Theorem

Andrew Fiori, Habiba Kadiri, Joshua Swidinsky

We provide very effective methods to convert both asymptotic and explicit numeric bounds on the prime counting function $ψ (x)$ to bounds of the same type on both $θ (x)$ and $π (x)$ .…

math.NT2022

Sharper bounds for the Chebyshev function $ψ (x)$

Andrew Fiori, Habiba Kadiri, Joshua Swidinsky

We improve the unconditional explicit bounds for the error term in the prime counting function $ψ (x)$ . In particular, we prove that, for all $x > 2$ , we have \[ \left| ψ(x)-x \right|…

math.NT2021★ 2 cited

Primes in the Chebotarev density theorem for all number fields

Habiba Kadiri, Peng-Jie Wong

We establish an explicit bound for the least prime occurring in the Chebotarev density theorem without any restriction. Let $L / K$ be any Galois extension of number fields such that…

math.NT2021

Explicit zero density for the Riemann zeta function

Habiba Kadiri, Allysa Lumley, Nathan Ng

Let $N (σ, T)$ denote the number of nontrivial zeros of the Riemann zeta function with real part greater than $σ$ and imaginary part between $0$ and $T$ . We provide explicit upper bo…

math.NT2020★ 6 cited

Short effective intervals containing primes in arithmetic progressions and the seven cubes problem

Habiba Kadiri

Let $q \geq 3$ be a non-exceptional modulus $q \geq 3$ , and let $a$ be a positive integer coprime with $q$ . For any $ε > 0$ , there exists $α > 0$ (computable), such that for all $x\ge α(\lo…

math.NT2020

Sharper Bounds for the Chebyshev function $θ (x)$

Samuel Broadbent, Habiba Kadiri, Allysa Lumley +2

In this article, we provide explicit bounds for the prime counting function $θ (x)$ in all ranges of $x$ . The bounds for the error term for $θ (x) - x$ are of the shape $ε x$ and $\fra…

math.NT2019

The least prime ideal in the Chebotarev Density Theorem

Habiba Kadiri, Nathan Ng, Peng-Jie Wong

In this article, we prove a new bound for the least prime ideal in the Chebotarev density theorem, which improves the main theorem of Zaman [Funct. Approx. Comment. Math. 57 (2017)…

math.NT2014★ 14 cited

Short effective intervals containing primes

Habiba Kadiri, Allysa Lumley

We prove that if $x$ is large enough, namely $x \geq x_{0}$ , then there exists a prime between $x (1 - Δ^{- 1})$ and $x$ , where $Δ$ is an effective constant computed in terms of $x_{0}$ . Th…

math.NT2014

A zero density result for the Riemann zeta function

Habiba Kadiri

In this article, we prove an explicit bound for $N (σ, T)$ , the number of zeros of the Riemann zeta function satisfying $σ < ℜ s < 1$ and $0 < ℑ s < T$ . This result provides a sig…

math.NT2013

New bounds for $ψ (x)$

Laura Faber, Habiba Kadiri

In this article we provide new explicit Chebyshev's bounds for the prime counting function $ψ (x)$ . The proof relies on two new arguments: smoothing the prime counting function whic…

math.NT2012

Explicit zero density theorems for Dedekind zeta functions

Habiba Kadiri, Nathan Ng

This article studies the zeros of Dedekind zeta functions. In particular, we establish a smooth explicit formula for these zeros and we derive an effective version of the Deuring-H…

math.NT2011

Explicit zero-free regions for Dedekind Zeta functions

Habiba Kadiri

Let K be a number field, n_K its degree, and d_K the absolute value of its discriminant. We prove that, if d_K is sufficiently large, then the Dedekind zeta function associated to…

math.NT2005★ 11 cited

An explicit zero-free region for the Dirichlet L-functions

Habiba Kadiri

Let $L (s, χ)$ be the Dirichlet $L$ -function associated to a non-principal primitive character $χ$ modulo $q$ with $3 \leq q \leq 400000$ . We prove a new explicit zero-free region for…

math.NT2004★ 26 cited

Une region explicite sans zero pour la fonction Zeta de Riemann

Habiba Kadiri

The Riemann Zeta function $ζ (s)$ never vanishes in the region : $ℜ s \geq 1 - \frac{1}{5.70176 lo g ∣ℑ s ∣} (∣ℑ s ∣ \geq 2) .$

Explicit Exponential Sum Estimates and Approximate Functional Equations for the Zeta Function

Bounds for Mertens Sums

An effective version of Chebotarev's density theorem

Comparative Prime Number Theory Problem List

Moments of L-functions Problem List

Sharper bounds for the error term in the Prime Number Theorem

Sharper bounds for the Chebyshev function ψ(x)

Primes in the Chebotarev density theorem for all number fields

Explicit zero density for the Riemann zeta function

Short effective intervals containing primes in arithmetic progressions and the seven cubes problem

Sharper Bounds for the Chebyshev function θ(x)

The least prime ideal in the Chebotarev Density Theorem

Short effective intervals containing primes

A zero density result for the Riemann zeta function

New bounds for ψ(x)

Explicit zero density theorems for Dedekind zeta functions

Explicit zero-free regions for Dedekind Zeta functions

An explicit zero-free region for the Dirichlet L-functions

Une region explicite sans zero pour la fonction Zeta de Riemann

Moments of $L$ -functions Problem List

Sharper bounds for the Chebyshev function $ψ (x)$

Sharper Bounds for the Chebyshev function $θ (x)$

New bounds for $ψ (x)$