7 papers
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…
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…
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…
Hardy-Littlewood-Riesz type equivalent criteria for the Generalized Riemann hypothesis
Meghali Garg, Bibekananda Maji
In the present paper, we prove that the generalized Riemann hypothesis for the Dirichlet -function is equivalent to the following bound: Let and be po…
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…