Sarah Peluse

activity

20142024

most citedStrings of special primes in arithmetic progressions

3 citations · 5 across the 4 of their papers we have counts for

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math.NT2024

Bounds in a popular multidimensional nonlinear Roth theorem

Sarah Peluse, Sean Prendiville, Xuancheng Shao

A nonlinear version of Roth's theorem states that dense sets of integers contain configurations of the form $x$ , $x + d$ , $x + d^{2}$ . We obtain a multidimensional version of this result…

math.NT2023★ 2 cited

Effective bounds for Roth's theorem with shifted square common difference

Sarah Peluse, Ashwin Sah, Mehtaab Sawhney

Let $S$ be a subset of ${1, \dots, N}$ avoiding the nontrivial progressions $x, x + y^{2} - 1, x + 2 (y^{2} - 1)$ . We prove that $∣ S ∣ ≪ N / lo g_{m} N$ , where $lo g_{m}$ is the $m$ -fold iterated…

math.NT2014

Congruence properties of Borcherds product exponents

Keenan Monks, Sarah Peluse, Lynnelle Ye

In his striking 1995 paper, Borcherds found an infinite product expansion for certain modular forms with CM divisors. In particular, this applies to the Hilbert class polynomial of…

math.NT2014★ 3 cited

Strings of special primes in arithmetic progressions

Keenan Monks, Sarah Peluse, Lynnelle Ye

The Green-Tao Theorem, one of the most celebrated theorems in modern number theory, states that there exist arbitrarily long arithmetic progressions of prime numbers. In a related…