Yuk-Kam Lau

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20162026

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math.NT2026

An asymptotic formula for primes of the form $u^{2} + v^{2} + 1$

Yujiao Jiang, Yuk-Kam Lau, Guangshi Lü

We prove Motohashi's conjecture on primes of the form $u^{2} + v^{2} + 1$ , with Iwaniec's corrected constant. Let $b$ denote the characteristic function of the positive integers representa…

math.NT2026

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…

math.NT2026

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…

An asymptotic formula for primes of the form u2+v2+1

Mixed moments of arithmetic functions and Kloosterman sums

Möbius Disjointness Conjecture for a skew product on a circle and the Heisenberg nilmanifold

An asymptotic formula for primes of the form $u^{2} + v^{2} + 1$