Hierarchical structure in the Trace Formula by Keating, JP

“…Motivated by recent developments in Random Matrix Theory and Number Theory, we elucidate a hierarchical structure in the way periodic orbits contribute to the Trace Formula that has implications for the value distribution of spectral determinants in quantum chaotic systems. …”

Arithmetic correlations over large finite fields by Keating, JP, Roditty-Gershon, E

“…The auto-correlations of arithmetic functions, such as the von Mangoldt function, the Mo bius function, and the divisor function, are the subject of classical problems in analytic number theory The function field analogs of these problems have recently been resolved in the limit of large finite field size q. …”

Joint moments of higher order derivatives of CUE characteristic polynomials I: asymptotic formulae by Keating, JP, Wei, F

“…Our conjectures are supported by comparison with results obtained previously in the number theory literature.…”

On the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L-functions in the Selberg class by Bui, HM, Keating, JP, Smith, DJ

“…This extends the results of Goldston and Montgomery [‘Pair correlation of zeros and primes in short intervals’, Analytic number theory and Diophantine problems (Stillwater, 1984), Progress in Mathematics 70 (1987) 183–203] and Montgomery and Soundararajan [‘Primes in short intervals’, Comm. …”