Primes in almost all short intervals. II

Danilo Bazzanella

Displaying similar documents to “Primes in almost all short intervals. II”

A note on primes between consecutive powers

Danilo Bazzanella (2009)

Rendiconti del Seminario Matematico della Università di Padova

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Links between $Δ (x, N) = \sum_{n \leq x N, (n, N) = 1} 1 - x ϕ (N)$ and character sums

P. Codecá, M. Nair (2003)

Bollettino dell'Unione Matematica Italiana

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We express $Δ (x, N)$ , as defined in the title, for $x = \frac{a}{q}$ and $q$ prime in terms of values of characters modulo $q$ . Using this, we show that the universal lower bound for $Δ (N) = {sup}_{x \in R} |Δ (x, N)|$ can, in general, be substantially improved when $N$ is composed of primes lying in a fixed residue class modulo $q$ . We also prove a corresponding improvement when $N$ is the product of the first s primes for infinitely many natural numbers $s$ .

On the ratio $f (t + c f^{- α} (t)) / f (t)$ .

Philip Hartman (1959)

Bollettino dell'Unione Matematica Italiana

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The sum of the first $n$ terms of an ${}_{5}F_{4}$ .

Leonard Carlitz (1964)

Bollettino dell'Unione Matematica Italiana

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Displaying similar documents to “Primes in almost all short intervals. II”

A note on primes between consecutive powers

Links between Δ ⁢ x , N = ∑ n ≤ x ⁢ N , n , N = 1 1 - x ⁢ ϕ ⁢ N and character sums

On the ratio f ⁢ t + c ⁢ f - α ⁢ t / f ⁢ t .

The sum of the first n terms of an F 4 5 .

Links between $Δ (x, N) = \sum_{n \leq x N, (n, N) = 1} 1 - x ϕ (N)$ and character sums

On the ratio $f (t + c f^{- α} (t)) / f (t)$ .

The sum of the first $n$ terms of an ${}_{5}F_{4}$ .