In 1998, she and her then adviser Jon Keating conjectured a value for the leading coefficient of the asymptotics of the moments of the Riemann zeta function.
The story makes reference to the Riemann hypothesis, featuring a sequence set in a 'world' modelled on the Riemann zeta function.
He has contributed to one of the discoveries concerning the Riemann zeta function, namely, that the Riemann zeros appear to display the same statistics as those which are believed to be present in energy levels of quantum chaotic systems and described by Random Matrix Theory.
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Alan M. Frieze showed that given a complete graph on n vertices, with edge weights that are independent identically distributed random variables with distribution function satisfying , then as n approaches +∞ the expected weight of the MST approaches , where is the Riemann zeta function.
Robert Langlands has cited Gaal's influence in his early investigations of zeta functions and Eisenstein series.