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…
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…
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…
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 normal…
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…
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…