Thomas Wright

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math.NT2026

$(a, a)$ -Carmichael numbers and greatest common divisors of $p - a$

Thomas Wright

Define an $(a, a)$ -Carmichael number to be a squarefree natural number $n$ such that $p ∣ n$ implies $p - a ∣ n - a$ . For such a number $n$ with prime factors $p_{1}, \dots, p_{m}$ , defi…

math.NT2025

A Shiu Theorem for Larger and Smoother Functions

Thomas Wright

In this paper, we broaden Shiu's Brun-Titchmarsh theorem to allow for functions that are larger and/or smooth-supported. In particular, let $f$ be a nonnegative multiplicative func…

math.NT2025

Primes in Arithmetic Progressions to Large Moduli and Siegel Zeroes

Thomas Wright

Let $I ¨ $ be a Dirichlet character mod $D$ with $L (s, I ¨ )$ its associated $L$ -function, and let $I ¨ (x, q, a)$ be Chebyshev's prime-counting function for primes congruent to $a$ modulo…

math.NT2024

Prime Distribution and Siegel Zeroes

Thomas Wright

Let $I ¨ $ be a Dirichlet character mod $D$ with $L (s, I ¨ )$ its associated $L$ -function, and let $I ¨ (x, q, a)$ be, as usual, Chebyshev's prime-counting function for the primes of the ar…

(a,a)-Carmichael numbers and greatest common divisors of p−a

A Shiu Theorem for Larger and Smoother Functions

Primes in Arithmetic Progressions to Large Moduli and Siegel Zeroes

Prime Distribution and Siegel Zeroes

$(a, a)$ -Carmichael numbers and greatest common divisors of $p - a$