Meghali Garg

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math.NT2023

Infinite families of solutions for $A^{3} + B^{3} = C^{3} + D^{3}$ and $A^{4} + B^{4} + C^{4} + D^{4} + E^{4} = F^{4}$

Archit Agarwal, Meghali Garg

Ramanujan, in his lost notebook, gave an interesting identity, which generates infinite families of solutions to Euler's Diophantine equation $A^{3} + B^{3} = C^{3} + D^{3}$ . In this paper…

math.NT2022

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 $L$ -function $L (s, χ)$ is equivalent to the following bound: Let $k \geq 1$ and $ℓ$ be po…

Infinite families of solutions for A3+B3=C3+D3 and A4+B4+C4+D4+E4=F4

Hardy-Littlewood-Riesz type equivalent criteria for the Generalized Riemann hypothesis

Infinite families of solutions for $A^{3} + B^{3} = C^{3} + D^{3}$ and $A^{4} + B^{4} + C^{4} + D^{4} + E^{4} = F^{4}$