Counting monic irreducible polynomials $P$ in ${\mathbb{F}_q[X]}$ for which order of ${X\!\!\hspace{4.44443pt}(\@mod \; P)}$ is odd

Christian Ballot

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A note on primes p with $σ (p^{m}) = z^{n}$

Maohua Le (1991)

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On systems of composite Lehmer numbers with prime indices

J. Wójcik (1996)

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A generalization of Scholz’s reciprocity law

Mark Budden, Jeremiah Eisenmenger, Jonathan Kish (2007)

Journal de Théorie des Nombres de Bordeaux

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We provide a generalization of Scholz’s reciprocity law using the subfields $K_{2^{t - 1}}$ and $K_{2^{t}}$ of $ℚ (ζ_{p})$ , of degrees $2^{t - 1}$ and $2^{t}$ over $ℚ$ , respectively. The proof requires a particular choice of primitive element for $K_{2^{t}}$ over $K_{2^{t - 1}}$ and is based upon the splitting of the cyclotomic polynomial $Φ_{p} (x)$ over the subfields.

On the number of representations in the Waring-Goldbach problem with a prime variable in an arithmetic progression

Maurizio Laporta (2012)

Journal de Théorie des Nombres de Bordeaux

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We prove a Bombieri-Vinogradov type theorem for the number of representations of an integer $N$ in the form $N = p_{1}^{g} + p_{2}^{g} + ... + p_{s}^{g}$ with $p_{1}, p_{2}, ..., p_{s}$ prime numbers such that $p_{1} \equiv l (\mod k)$ , under suitable hypothesis on $s = s (g)$ for every integer $g \geq 2$ .

Restriction theory of the Selberg sieve, with applications

Ben Green, Terence Tao (2006)

Journal de Théorie des Nombres de Bordeaux

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The Selberg sieve provides majorants for certain arithmetic sequences, such as the primes and the twin primes. We prove an $L^{2}$ – $L^{p}$ restriction theorem for majorants of this type. An immediate application is to the estimation of exponential sums over prime $k$ -tuples. Let $a_{1}, \dots, a_{k}$ and $b_{1}, \dots, b_{k}$ be positive integers. Write $h (θ) : = \sum_{n \in X} e (n θ)$ , where $X$ is the set of all $n \leq N$ such that the numbers $a_{1} n + b_{1}, \dots, a_{k} n + b_{k}$ are all prime. We obtain upper bounds for ${∥ h ∥}_{L^{p} (𝕋)}$ , $p > 2$ , which are (conditionally on the Hardy-Littlewood prime tuple conjecture) of the correct...

Displaying similar documents to “Counting monic irreducible polynomials P in 𝔽 q [ X ] for which order of X ( mod P ) is odd”

A note on primes p with σ ( p m ) = z n

On systems of composite Lehmer numbers with prime indices

A generalization of Scholz’s reciprocity law

On the number of representations in the Waring-Goldbach problem with a prime variable in an arithmetic progression

Restriction theory of the Selberg sieve, with applications

Displaying similar documents to “Counting monic irreducible polynomials $P$ in $𝔽_{q} [X]$ for which order of $X (mod P)$ is odd”

A note on primes p with $σ (p^{m}) = z^{n}$