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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…
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 divisor generating -series and cumulants arising from random graphs
Archit Agarwal, Subhash Chand Bhoria, Pramod Eyyunni +2
Uchimura, in 1987, introduced a probability generating function for a random variable and using properties of this function he discovered an interesting -series identity. He…
Laurent series expansions of -functions
Tushar Karmakar, Saikat Maity, Bibekananda Maji
One of the main objectives of the current paper is to revisit the well known Laurent series expansions of the Riemann zeta function , Hurwitz zeta function and Diric…