10 papers
Diophantine approximation by primes and Landau--Siegel zeros
Sun-Kai Leung, Stelios Sachpazis
Let be an irrational number of finite type and let . Assuming the infinitude of Siegel zeros (respectively, sufficiently strong Siegel zeros), we show that fo…
Extreme values of central -derivatives and heights of Heegner points
Mohammad H. Hamdar, Sun-Kai Leung
Using Soundararajan's resonance method, we obtain extreme values of the central derivatives \[ L^{(r)}(1/2,f\otimesχ_d), \] where is a normalized newform and ranges over…
Low moments of automorphic random multiplicative function sums
Sun-Kai Leung
We determine the order of the low moments of partial sums of random multiplicative functions associated with Euler products of bounded degree whose unitary local parameters satisfy…
Low moments of Hecke eigenvalue sums
Jad Hamdan, Sun-Kai Leung, Mo Dick Wong
We show that partial sums of the Sato--Tate random multiplicative functions introduced by Cogdell and Michel exhibit better-than-square-root cancellation. The proof proceeds via a…
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 prove that there always exists an arithmetic progression with common difference for which the -th least pri…
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…