4 papers
math.NT2025
Exponential sums with polynomials and their applications to primes in sparse sets
Lingyu Guo, Victor Zhenyu Guo, Mengyao Jing
Exponential sums with monomials are highly related to many interesting problems in number theory and well studied by many literatures. In this paper, we consider the exponential su…
math.NT2025
Additive problems on
Lingyu Guo, Victor Zhenyu Guo, Li Lu
The sequence is an important subsequence of the well-known Piatetski-Shapiro sequence,…
math.NT2025
The Piatetski-Shapiro prime number theorem
Lingyu Guo, Victor Zhenyu guo, Li Lu
The Piatetski-Shapiro sequences are of the form , where is the integer part. It is expected that th…
math.NT2025
Improvements on exponential sums related to Piatetski-Shapiro primes
Li Lu, Lingyu Guo, Victor Z. Guo
We prove a new bound to the exponential sum of the form $$ \sum_{h \sim H}δ_h \mathop{\sum_{m\sim M}\sum_{n\sim N}}_{mn\sim x}a_{m}b_{n}\e\big(αmn + h(mn + u)^γ\big), $$ by a new a…