Browsing Waterloo Research by Author "Kuo, Wentang"
Now showing items 1-9 of 9
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The asymptotic estimates and Hasse principle for multidimensional Waring's problem
Kuo, Wentang; Liu, Yu-Ru; Zhao, Xiaomei (Elsevier, 2019-09-07)Motivated by the asymptotic estimates and Hasse principle for multidimensional Waring's problem via the circle method, we prove for the first time that the corresponding singular series is bounded below by an absolute ... -
A Carlitz module analogue of a conjecture of Erdos and Pomerance
Kuo, Wentang; Liu, Yu-Ru (American Mathematical Society, 2009-09)Abstract. Let A = Fq[T] be the ring of polynomials over the finite field Fq and 0 = a ∈ A. Let C be the A-Carlitz module. For a monic polynomial m ∈ A, let C(A/mA) and ¯a be the reductions of C and a modulo mA respectively. ... -
Cyclicity of finite Drinfeld modules
Kuo, Wentang; Liu, Yu-Ru (Wiley, 2009-12)Le tA=Fq[T] be the polynomial ring over the finite field Fq,letk=Fq(T) be the rational function field, and let K be a finite extension of k. For a prime P of K, we denote by OP the valuation ring of P, by MP the maximal ... -
The Erdős–Kac theorem and its generalizations
Kuo, Wentang; Liu, Yu-Ru (American Mathematical Society, 2008)Abstract. We give a survey of the Erd}o-Kac theorem and its various generalizations. In particular, we discuss an open conjecture of Erd}os and Pomerance about the distribution of the number of distinct prime divisors of ... -
Gaussian Laws on Drinfeld Modules
Kuo, Wentang; Liu, Yu-Ru (World Scientific, 2009)Let A = 𝔽q[T] be the polynomial ring over the finite field 𝔽q, k = 𝔽q(T) the rational function field, and K a finite extension of k. Let ϕ be a Drinfeld A-module over K of rank r. For a place 𝔓 of K of good reduction, ... -
Multidimensional Vinogradov-type Estimates in Function Fields
Kuo, Wentang; Liu, Yu-Ru; Zhao, Xiaomei (Cambridge University Press, 2014)Let Fq[t] denote the polynomial ring over the finite field Fq. We employ Wooley’s new efficient congruencing method to prove certain multidimensional Vinogradov-type estimates in Fq[t]. These results allow us to apply a ... -
On the number of irreducible factors with a given multiplicity in function fields
Das, Sourabhashis; Elma, Ertan; Kuo, Wentang; Liu, Yu-Ru (Elsevier, 2023-12)Let k ≥ 1 be a natural number and f ∈ Fq[t] be a monic polynomial. Let ωk(f) denote the number of distinct monic irreducible factors of f with multiplicity k. We obtain asymptotic estimates for the first and the second ... -
The Shifted Turan Sieve Method on Tournaments
Kuo, Wentang; Liu, Yu-Ru; Ribas, Savio; Zhou, Kevin (Cambridge University Press, 2019)Abstract. We construct a shi ed version of the Turán sieve method developed by R. Murty and the second author and apply it to counting problems on tournaments. More precisely, we obtain upper bounds for the number of ... -
The shifted Turan sieve method on tournaments II
Kuo, Wentang; Liu, Yu-Ru; Ribas, Savio; Zhou, Kevin (Elsevier, 2021-12)In a previous work [5], we developed the shifted Turán sieve method on a bipartite graph and applied it to problems on cycles in tournaments. More precisely, we obtained upper bounds for the number of tournaments which ...