Mayank Pandey

activity

20222026

most citedPartial sums of typical multiplicative functions over short moving intervals

6 citations · 6 across the 7 of their papers we have counts for

collaborators

9 papers

cs.RO2026

Targeted Modality Dropout for Real-Robot Manipulation Robust to Intermittent Vision Loss

Genki Shikada, Kazuki Osamura, Masaru Ide +2

Imitation learning policies that integrate multiple sensory modalities are prone to overreliance on a dominant modality, such as vision, during training, which can disrupt policy e…

math.NT2026

The sixth moment of the Riemann zeta function

Alexandre de Faveri, Mayank Pandey

We prove new large value estimates for the Riemann zeta function on the critical line. For instance, we improve the upper bound on the measure of $t \in [T, 2 T]$ with $|ζ(1/2 + it)|…

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{…

math.NT2022★ 6 cited

Partial sums of typical multiplicative functions over short moving intervals

Mayank Pandey, Victor Y. Wang, Max Wenqiang Xu

We prove that the $k$ -th positive integer moment of partial sums of Steinhaus random multiplicative functions over the interval $(x, x + H]$ matches the corresponding Gaussian moment…

Targeted Modality Dropout for Real-Robot Manipulation Robust to Intermittent Vision Loss

The sixth moment of the Riemann zeta function

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

Partial sums of typical multiplicative functions over short moving intervals

$L^{1}$ 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