Thomas Wright

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20232026

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math.NT2026

Primes in arithmetic progressions and Siegel zeroes

Thomas Wright

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

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 $x$ be a large parameter, and let $f_x(n…

math.NT2025

Primes in Arithmetic Progressions to Large Moduli and Siegel Zeroes

Thomas Wright

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

math.NT2024

Carmichael numbers and least common multiples of $p - 1$

Thomas Wright

For a Carmichael number $n$ with prime factors $p_{1}, \dots, p_{m}$ , define $K = GC D [p_{1} - 1, \dots, p_{m} - 1],$ and let $C_{ν} (X)$ denote the number of Carmichael numbers up to $X$ such that…

math.NT2023

Prime Distribution and Siegel Zeroes

Thomas Wright

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

Primes in arithmetic progressions and Siegel zeroes

(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

Carmichael numbers and least common multiples of p−1

Prime Distribution and Siegel Zeroes

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

Carmichael numbers and least common multiples of $p - 1$