Shashi Chourasiya

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20212025

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math.NT2025

An explicit form of Ingham's zero density estimate

Shashi Chourasiya, Aleksander Simonič

Ingham (1940) proved that $N (σ, T) ≪ T^{3 (1 - σ) / (2 - σ)} lo g^{5} T$ , where $N (σ, T)$ counts the number of the non-trivial zeros $ρ$ of the Riemann zeta-function with $\Re\{ρ\}\geqσ\ge…

math.NT2025

Power-free palindromes and reversed primes

Shashi Chourasiya, Daniel R. Johnston

We prove new results related to the digital reverse $n$ of a positive integer $n$ in a fixed base $b$ . First we show that for $b \geq 26000$ , there exists infinitely…

math.NT2024

An explicit version of Carlson's theorem

Shashi Chourasiya

Let $N (σ, T)$ denote the number of nontrivial zeros of the Riemann zeta function with real part greater than $σ$ and imaginary part lying between $0$ and $T$ . In this article, we pr…

math.NT2021

A new Ramanujan-type identity for $L (2 k + 1, χ_{1})$

Shashi Chourasiya, Md Kashif Jamal, Bibekananda Maji

One of the celebrated formulas of Ramanujan is about odd zeta values, which has been studied by many mathematicians over the years. A notable extension was given by Grosswald in 19…

An explicit form of Ingham's zero density estimate

Power-free palindromes and reversed primes

An explicit version of Carlson's theorem

A new Ramanujan-type identity for L(2k+1,χ1​)

A new Ramanujan-type identity for $L (2 k + 1, χ_{1})$