7 papers · 1 filter
An asymptotic formula for primes of the form
Yujiao Jiang, Yuk-Kam Lau, Guangshi Lü
We prove Motohashi's conjecture on primes of the form , with Iwaniec's corrected constant. Let denote the characteristic function of the positive integers representa…
Mixed moments of arithmetic functions and Kloosterman sums
Yujiao Jiang, Yuk-Kam Lau
We extend the Nair--Tenenbaum estimates for short sums of nonnegative arithmetic functions at polynomial values to mixed moments involving Kloosterman sums. Combining these estimat…
Möbius Disjointness Conjecture for a skew product on a circle and the Heisenberg nilmanifold
Yuk-Kam Lau, Jing Ma
We establish Sarnak's conjecture on Möbius disjointness for the dynamical system of a skew product on a circle and the three-dimensional Heisenberg nilmanifold, first studied by We…
Prime detecting quasi-modular forms in higher level
Ben Kane, Krishnarjun Krishnamoorthy, Yuk-Kam Lau
In a previous work, the authors resolved a conjecture about the structure of prime-detecting quasi-modular forms by studying sign changes occurring in quasi-modular cusp forms. In…
On a conjecture about prime-detecting quasimodular forms
Ben Kane, Krishnarjun Krishnamoorthy, Yuk-Kam Lau
Motivated by weighted partition of that vanish if and only if is a prime, Craig, van Ittersum, and Ono conjecture a classification of quasimodular forms which detect primes…
Divisor problems for restricted Fourier coefficients of modular forms
Yuk-Kam Lau, Wonwoong Lee
Let be the number of divisors of . We investigate the average value of for a positive integer and the -th Fourier coefficient of a cuspidal…
On Fourier coefficients of modular forms of half integral weight at squarefree integers
Y. -J Jiang, Y. -K Lau, Emmanuel Royer +1
We show that the Dirichlet series associated to the Fourier coefficients of a half-integral weight Hecke eigenform at squarefree integers extends analytically to a holomorphic func…