3 papers
math.NT2025
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…
math.NT2025
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…
math.NT2024
Equivalent criteria for the Riemann hypothesis for a general class of -functions
Meghali Garg, Bibekananda Maji
In 1916, Riesz gave an equivalent criterion for the Riemann hypothesis (RH). Inspired from Riesz's criterion, Hardy and Littlewood showed that RH is equivalent to the following bou…