In symbolic logic, non-standard numbers is common nomenclature for a model of numbers which satisfies the axioms of some arithmetical system, but doesn't consist of what people would normally think of as numbers. For instance, a 'number' which is its own successor is a non-standard number, and so are the pair of 'numbers' $a$ and $b$ which are each others successor (these can be considered in $Q$, Robinsons arithmetic).
I was wondering if anyone had conducted research into the Riemann hypothesis using non standard numbers, and if so, what the results tell us. Is there anything interesting to learn from this endeavour, was the Riemann hypothesis found to be false in certain non-standard models? If so, what did these models look like?