Diksha Rani Bansal

activity

20242026

collaborators

4 papers

math.NT2026

An extension of Ramanujan-Guinand identity for the Dedekind zeta function and a new formula for $ζ_{F} (2)$ and $ζ_{F} (2 m + 1)$

Diksha Rani Bansal, Bibekananda Maji

On page 253 of his Lost Notebook, Ramanujan recorded an intriguing identity relating a generalized divisor function and a modified Bessel function, which was later rediscovered by…

math.NT2025

Analogues of Harglotz-Zagier-Novikov function

Diksha Rani Bansal, Bibekananda Maji, Pragya Singh

Recently, Choie and Kumar extensively studied the Herglotz-Zagier-Novikov function $F (z; u, v)$ , defined as \begin{align*} \mathfrak{F}(z;u,v) = \int_{0}^{1} \frac{\log(1-…

math.NT2025

Number Field Analogue of Jacobi Theta Relation And Zeros of Dedekind zeta function on Re $(s) = 1/2$

Diksha Rani Bansal, Bibekananda Maji

In 1914, Hardy proved that there are infinitely many non-trivial zeros of the Riemann zeta function $I^¶ (s)$ on the critical line Re $(s) = 1/2$ using the Jacobi theta relation. In thi…

math.NT2024

A Number Field Analogue of Ramanujan's identity for $I^¶ (2 m + 1)$

Diksha Rani Bansal, Bibekananda Maji

Ramanujan's famous formula for $I^¶ (2 m + 1)$ has captivated the attention of numerous mathematicians over the years. Grosswald, in 1972, found a simple extension of Ramanujan's formul…

An extension of Ramanujan-Guinand identity for the Dedekind zeta function and a new formula for ζF​(2) and ζF​(2m+1)

Analogues of Harglotz-Zagier-Novikov function

Number Field Analogue of Jacobi Theta Relation And Zeros of Dedekind zeta function on Re(s)=1/2

A Number Field Analogue of Ramanujan's identity for I^¶(2m+1)

An extension of Ramanujan-Guinand identity for the Dedekind zeta function and a new formula for $ζ_{F} (2)$ and $ζ_{F} (2 m + 1)$

Number Field Analogue of Jacobi Theta Relation And Zeros of Dedekind zeta function on Re $(s) = 1/2$

A Number Field Analogue of Ramanujan's identity for $I^¶ (2 m + 1)$