Roupam Ghosh

activity

20082010

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3 papers · 1 filter

math.GM2009

A new criterion of the Riemann hypothesis

Roupam Ghosh

We introduce a new criterion which if satisfied implies the Riemann hypothesis.

math.GM2009

An equation satisfied by all non-trivial zeros $ρ$ of the Riemann zeta function $ζ$

Roupam Ghosh

We show that if $ρ$ is a non-trivial zero of the Riemann zeta function $ζ$ then $2^{ρ} + \frac{1}{ρ - 1} + 1/2 = ρ \int_{1}^{\infty} t + 1/2 t^{- ρ - 1} d t$ where, $x$ is the fractio…

math.GM2009

New lower bounds for the size of a non-trivial loop in the Collatz 3x+1 and generalized px+q problem

Roupam Ghosh

In the Collatz 3x+1 problem, there are 3 possibilities: Starting from any positive number, we either reach the trivial loop (1,4,2), end up in a non-trivial loop, or go until infin…

A new criterion of the Riemann hypothesis

An equation satisfied by all non-trivial zeros ρ of the Riemann zeta function ζ

New lower bounds for the size of a non-trivial loop in the Collatz 3x+1 and generalized px+q problem

An equation satisfied by all non-trivial zeros $ρ$ of the Riemann zeta function $ζ$