Relation/use of irrational or transcedental numbers in computer science?
On the surface that does not strike me as a high-quality paper.  I wouldn't recommend it.

I don't think irrational/transcendental numbers are a good approach to building PRNGs.  Building PRNGs is tricky business.  There are standard PRNGs; I suggest using one of them, rather than trying to invent your own.  They all ensure that the output is extremely unlikely to repeat within any reasonable time period.

There is no one theory of irrational/transcendental numbers, and not just one connection to CS; irrational numbers show up in a variety of areas of CS.  It's not feasible to give you a complete list; such a list would be far too long.  If you just want one example, you might read about the Fibonacci numbers and their connection to the golden ratio (which is an irrational number).