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math.NT2026
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
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 ne…
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…