6 papers
Piatetski-Shapiro Primes in short intervals
Lingyu Guo, Victor Zhenyu Guo
The existence of primes in a short interval, which asks if there are prime numbers in the interval , is a core problem in number theory. Guth and Maynard proved the b…
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…
Additive problems on
Lingyu Guo, Victor Zhenyu Guo, Li Lu
The sequence is an important subsequence of the well-known Piatetski-Shapiro sequence,…
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…
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…
On a conjecture of R. M. Murty and V. K. Murty II
Yuchen Ding, Victor Zhenyu Guo, Yu Zhang
Let be the number of primes such that divides . Assuming the Elliott--Halberstam Conjecture, we prove a conjecture posted by M. R. Murty and V. K. Murty in 20…