6 papers
The Dirichlet series that generates the Möbius function is the inverse of the Riemann zeta function in the right half of the critical strip
Roupam Ghosh
In this paper I introduce a criterion for the Riemann hypothesis, and then using that I prove converges for . I use a step functi…
On integrals of fractional parts and the theory of prime differences
Roupam Ghosh
In this paper we study the integrals of fractional parts of given functions, and develop some new tools to understand the behaviour of prime differences. We demonstrate how simply…
A new criterion of the Riemann hypothesis
Roupam Ghosh
We introduce a new criterion which if satisfied implies the Riemann hypothesis.
An equation satisfied by all non-trivial zeros of the Riemann zeta function
Roupam Ghosh
We show that if is a non-trivial zero of the Riemann zeta function then where, is the fractio…
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…
On the Collatz Problem
Roupam Ghosh
Taking a new approach towards analyzing the Collatz Problem, or, 3x+1 conjecture. Introducing some new functions, the Collatz-2 and Collatz-3 sequences, as well as deducing results…