5 papers · 1 filter
A Combinatorial Proof of Partition Identities for the Number of Distinct Part Sizes
Archit Agarwal, Meghali Garg
In 1984, Bressoud and Subbarao established an interesting weighted partition identity connecting the partition function and the divisor function. Recently, the first author, jointl…
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…
Infinite families of solutions for and
Archit Agarwal, Meghali Garg
Ramanujan, in his lost notebook, gave an interesting identity, which generates infinite families of solutions to Euler's Diophantine equation . In this paper…
Riesz-type criteria for the Riemann hypothesis
Archit Agarwal, Meghali Garg, Bibekananda Maji
In 1916, Riesz proved that the Riemann hypothesis is equivalent to the bound $\sum_{n=1}^\infty \frac{μ(n)}{n^2} \exp\left( - \frac{x}{n^2} \right) = O_ε \left( x^{-\frac{3}{4} + ε…