6 papers
A central limit theorem for prime geodesics on random surfaces of large genus
Sun-Kai Leung
We show that, for Weil--Petersson random closed hyperbolic surfaces of large genus, the normalized weighted count of prime geodesics with norm in the interval is asymptot…
Visiting early at prime times
Tony Haddad, Sun-Kai Leung, Cihan Sabuncu
Given an integer and a sufficiently large , we apply a variant of the Maynard--Tao sieve weight to establish the existence of an arithmetic progression with common di…
Pseudorandomness of primes at large scales
Sun-Kai Leung
Assuming a -variant of the prime -tuple conjecture uniformly, we compute mixed moments of the number of primes in disjoint short intervals and progressions, respectively. Thi…
A central limit theorem for coefficients of -functions in short intervals
Sun-Kai Leung
Assuming the generalized Lindelöf hypothesis (GLH), a weak version of the generalized Ramanujan conjecture and a Rankin--Selberg type partial sum estimate, we establish the normali…
Moments of primes in progressions to a large modulus
Sun-Kai Leung
Assuming a uniform -variant of the prime -tuple conjecture, we compute moments of the number of primes in arithmetic progressions to a large modulus as the residue classe…
Joint distribution of primes in multiple short intervals
Sun-Kai Leung
Assuming the Riemann hypothesis (RH) and the linear independence conjecture (LI), we show that the weighted count of primes in multiple short intervals follows a multivariate Gauss…