5 papers
A number field extension of Ramanujan's identity and its integral representation via the generalized Riemann -function
Diksha Rani Bansal
On pages 219--220 of Ramanujan's Lost Notebook appears an intriguing modular transformation whose integral representation is expressed in terms of the Riemann -function. In this…
An extension of Ramanujan-Guinand identity for the Dedekind zeta function and a new formula for and
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…
Analogues of Harglotz-Zagier-Novikov function
Diksha Rani Bansal, Bibekananda Maji, Pragya Singh
Recently, Choie and Kumar extensively studied the Herglotz-Zagier-Novikov function , defined as \begin{align*} \mathfrak{F}(z;u,v) = \int_{0}^{1} \frac{\log(1-…
Number Field Analogue of Jacobi Theta Relation And Zeros of Dedekind zeta function on Re
Diksha Rani Bansal, Bibekananda Maji
In 1914, Hardy proved that there are infinitely many non-trivial zeros of the Riemann zeta function on the critical line Re using the Jacobi theta relation. In this…
A Number Field Analogue of Ramanujan's identity for
Diksha Rani Bansal, Bibekananda Maji
Ramanujan's famous formula for has captivated the attention of numerous mathematicians over the years. Grosswald, in 1972, found a simple extension of Ramanujan's formula…