13 papers · 1 filter
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-…
Rademacher-type exact formula and higher order Turán inequalities for -colored -regular partitions
Archit Agarwal, Meghali Garg, Bibekananda Maji
In 1937, Rademacher refined the circle method of Hardy and Ramanujan to derive an exact convergent series for the partition function . In 1942, Hua derived an exact formula f…
Rademacher-type exact formula and higher order Turán inequalities for cubic overpartitions
Archit Agarwal, Meghali Garg, Bibekananda Maji
In 1918, Hardy and Ramanujan made a breakthrough by developing the circle method to deduce an asymptotic formula for the partition function , which was later refined by Radem…
Voronoi summation formula for the generalized divisor function
Atul Dixit, Bibekananda Maji, Akshaa Vatwani
For a fixed and a fixed , let denote the sum of -th powers of those divisors of whose -th powers also divide . T…
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 thi…