Sourabhashis Das

collaborators

9 papers

math.NT2025

On the distribution of the total number of generators of $h$ -free and $h$ -full elements in an abelian monoid

Sourabhashis Das, Wentang Kuo, Yu-Ru Liu

Let $m$ be an element of an abelian monoid, with $Ω (m)$ denoting the total number of prime elements generating $m$ . We study the moments of $Ω(\mat…

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.NT2025

New zero-free regions for Dedekind zeta-functions at small and large ordinates

Sourabhashis Das, Swati Gaba, Ethan Simpson Lee +2

Given a number field $L \neq = Q$ , we obtain new and explicit zero-free regions for Dedekind zeta-functions of $L$ , which refine the previous works of Ahn--Kwon, Kadiri, and…

math.NT2025

A subset generalization of the Erdős-Kac theorem over number fields with applications

Sourabhashis Das, Wentang Kuo, Yu-Ru Liu

Let $ω (n)$ denote the number of distinct prime factors of a natural number $n$ . In 1940, Erdős and Kac established that $ω (n)$ obeys the Gaussian distribution over natural numbers.…

math.NT2025

Generalizations of Erdős-Kac theorem with applications

Sourabhashis Das, Wentang Kuo, Yu-Ru Liu

Let $ω (n)$ denote the number of distinct prime factors of a natural number $n$ . In 1940, Erdős and Kac established that $ω (n)$ obeys the Gaussian distribution over natural numbers,…

math.NT2025

On the distribution of the number of distinct generators of h-free and h-full elements in an abelian monoid

Sourabhashis Das, Wentang Kuo, Yu-Ru Liu

This work introduces the first in-depth study of h-free and h-full elements in abelian monoids, providing a unified approach for understanding their role in various mathematical st…

math.NT2024

On limiting distributions of arithmetic functions

Sourabhashis Das

For a natural number n, let M(n) denote the maximum exponent of any prime power dividing n, and let m(n) denote the minimum exponent of any prime power dividing n. We study the sec…

math.NT2024

On the number of prime factors with a given multiplicity over h-free and h-full numbers

Sourabhashis Das, Wentang Kuo, Yu-Ru Liu

Let $k$ and $n$ be natural numbers. Let $ω_{k} (n)$ denote the number of distinct prime factors of $n$ with multiplicity $k$ as studied by Elma and the third author. We obtain asympto…

math.NT2024

Distribution of $ω (n)$ over $h$ -free and $h$ -full numbers

Sourabhashis Das, Wentang Kuo, Yu-Ru Liu

Let $ω (n)$ denote the number of distinct prime factors of a natural number $n$ . In 1917, Hardy and Ramanujan proved that $ω (n)$ has normal order $lo g lo g n$ over naturals. In thi…

On the distribution of the total number of generators of h-free and h-full elements in an abelian monoid

An effective version of Chebotarev's density theorem

New zero-free regions for Dedekind zeta-functions at small and large ordinates

A subset generalization of the Erdős-Kac theorem over number fields with applications

Generalizations of Erdős-Kac theorem with applications

On the distribution of the number of distinct generators of h-free and h-full elements in an abelian monoid

On limiting distributions of arithmetic functions

On the number of prime factors with a given multiplicity over h-free and h-full numbers

Distribution of ω(n) over h-free and h-full numbers

On the distribution of the total number of generators of $h$ -free and $h$ -full elements in an abelian monoid

Distribution of $ω (n)$ over $h$ -free and $h$ -full numbers