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The Burgess inequality and the least kth power non-residue

- Enrique Treviño
- Mathematics
- 9 December 2014

The Burgess inequality is the best upper bound we have for incomplete character sums of Dirichlet characters. In 2006, Booker gave an explicit estimate for quadratic Dirichlet characters which he… Expand

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The least k-th power non-residue

- Enrique Treviño
- Mathematics
- 1 April 2015

Abstract Let p be a prime number and let k ≥ 2 be a divisor of p − 1 . Norton proved that the least k-th power non-residue mod p is at most 3.9 p 1 / 4 log p unless k = 2 and p ≡ 3 ( mod 4 ) , in… Expand

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The least kth power non-residue I

- Enrique Treviño
- 2011

Let p be a prime number and let k ≥ 2 be an integer such that k divides p − 1. Norton proved that the least k-th power non-residue modp is at most 3.9p log p unless k = 2 and p ≡ 3 (mod 4), in which… Expand

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The Primes that Euclid Forgot

- P. Pollack, Enrique Treviño
- Mathematics, Computer Science
- Am. Math. Mon.
- 1 May 2014

TLDR

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On the sum of $k$-th powers in terms of earlier sums

- S. Miller, Enrique Treviño
- Mathematics
- 16 December 2019

For $k$ a positive integer let $S_k(n) = 1^k + 2^k + \cdots + n^k$, i.e., $S_k(n)$ is the sum of the first $k$-th powers. Faulhaber conjectured (later proved by Jacobi) that for $k$ odd, $S_k(n)$… Expand

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The multidimensional Frobenius problem

- Jeff Amos, I. Pascu, V. Ponomarenko, Enrique Treviño, Y. Zhang
- Mathematics
- 31 December 2011

Consider the problem of determining maximal vectors g such that the Diophantine system Mx = g has no solution. We provide a variety of results to this end: conditions for the existence of g,… Expand

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The least inert prime in a real quadratic field

- Enrique Treviño
- Computer Science, Mathematics
- Math. Comput.
- 1 September 2012

TLDR

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Numerically explicit estimates for character sums

- Enrique Treviño
- Mathematics
- 2011

Character sums make their appearance in many number theory problems: showing that there are infinitely many primes in any coprime arithmetic progression, estimating the least quadratic non-residue,… Expand

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Resolving Grosswald's conjecture on GRH

- Kevin J. McGown, Enrique Treviño, T. Trudgian
- Mathematics
- 21 August 2015

In this paper we examine Grosswald's conjecture on $g(p)$, the least primitive root modulo $p$. Assuming the Generalized Riemann Hypothesis (GRH), and building on previous work by Cohen, Oliveira e… Expand

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ON THE MAXIMUM NUMBER OF CONSECUTIVE INTEGERS ON WHICH A CHARACTER IS CONSTANT

- Enrique Treviño
- 2012

Let χ be a non-principal Dirichlet character to the prime modulus p. In 1963, Burgess showed that the maximum number of consecutive integers H for which χ remains constant is O ( p1/4 log p ) . This… Expand

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