Mayank Pandey

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20222026

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math.NT2026

Exponential sums over primes

James Maynard, Mayank Pandey, Maksym Radziwiłł

Let $α = a / q + ε$ with $(a, q) = 1$ , $q \leq N^{1/2}$ and $∣ ε ∣ \leq 1/ (q N^{1/2})$ , and let $B := max (q, q N ∣ ε ∣)$ . We show that \[ \Bigl|\sum_{n<N}Λ(n)e(nα)\Bigr|\le N^{o(1)}\Bigl(\frac{N}{B^{1/2…

math.NT2025

$L^{1}$ means of exponential sums with multiplicative coefficients. II

Mayank Pandey, Maksym Radziwiłł

Let $f$ be a real-valued $1$ -bounded multiplicative function. Suppose that the mean-value of $f^{2}$ exists, and $$\int_{0}^{1} \Big | \sum_{n \leq N} f(n)e^{2πi n α} \Big | d α\le…

math.NT2023

Numbers with at most $2$ prime factors in short arithmetic progressions

Mayank Pandey

We show that if $\frac{L}{φ ( q ) l o g X} \to \infty$ as $X \to \infty$ , almost all $(a, x) \in (Z / q Z)^{\times} \times [X, 2 X]$ are such that there exists a product of at most…

math.NT2023

$L^{1}$ means of exponential sums with multiplicative coefficients. I

Mayank Pandey, Maksym Radziwiłł

We show that the $L^{1}$ norm of an exponential sum of length $X$ and with coefficients equal to the Liouville or Möbius function is at least $\gg_{\varepsilon} X^{1/4 - \varepsilon}…

math.NT2023

Small scale distribution of linear patterns of primes

Mayank Pandey, Katharine Woo

Let $Ψ$ be a system of linear forms with finite complexity. In their seminal paper, Green and Tao showed the following prime number theorem for values of the system $Ψ$ : $$\sum_{x\…

math.NT2022

On the length of Pierce expansions

Zachary Chase, Mayank Pandey

For a given positive integer $n$ , how long can the process $x \mapsto n (mod x)$ last before reaching $0$ ? We improve Erdős and Shallit's upper bound of $O(n^{\frac{…

Exponential sums over primes

L1 means of exponential sums with multiplicative coefficients. II

Numbers with at most 2 prime factors in short arithmetic progressions

L1 means of exponential sums with multiplicative coefficients. I

Small scale distribution of linear patterns of primes

On the length of Pierce expansions

$L^{1}$ means of exponential sums with multiplicative coefficients. II

Numbers with at most $2$ prime factors in short arithmetic progressions

$L^{1}$ means of exponential sums with multiplicative coefficients. I