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

Maurizio Laporta

Displaying similar documents to “On the number of representations in the Waring-Goldbach problem with a prime variable in an arithmetic progression”

On the parity of generalized partition functions, III

Fethi Ben Saïd, Jean-Louis Nicolas, Ahlem Zekraoui (2010)

Journal de Théorie des Nombres de Bordeaux

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Improving on some results of J.-L. Nicolas [], the elements of the set $𝒜 = 𝒜 (1 + z + z^{3} + z^{4} + z^{5})$ , for which the partition function $p (𝒜, n)$ (i.e. the number of partitions of $n$ with parts in $𝒜$ ) is even for all $n \geq 6$ are determined. An asymptotic estimate to the counting function of this set is also given.

An arithmetic formula of Liouville

Erin McAfee, Kenneth S. Williams (2006)

Journal de Théorie des Nombres de Bordeaux

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An elementary proof is given of an arithmetic formula, which was stated but not proved by Liouville. An application of this formula yields a formula for the number of representations of a positive integer as the sum of twelve triangular numbers.

Factorization problems in class number two

Franz Halter-Koch (1993)

Colloquium Mathematicae

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CM liftings of supersingular elliptic curves

Ben Kane (2009)

Journal de Théorie des Nombres de Bordeaux

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Assuming GRH, we present an algorithm which inputs a prime $p$ and outputs the set of fundamental discriminants $D < 0$ such that the reduction map modulo a prime above $p$ from elliptic curves with CM by $𝒪_{D}$ to supersingular elliptic curves in characteristic $p$ is surjective. In the algorithm we first determine an explicit constant $D_{p}$ so that $| D | > D_{p}$ implies that the map is necessarily surjective and then we compute explicitly the cases $| D | < D_{p}$ .

A combinatorial identity arising from cobordism theory.

Gijswijt, D., Moree, P. (2005)

Acta Mathematica Universitatis Comenianae. New Series

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Inequalities concerning the function π(x): Applications

Laurenţiu Panaitopol (2000)

Acta Arithmetica

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Introduction. In this note we use the following standard notations: π(x) is the number of primes not exceeding x, while $θ (x) = \sum_{p \leq x} l o g p$ . The best known inequalities involving the function π(x) are the ones obtained in [6] by B. Rosser and L. Schoenfeld: (1) x/(log x - 1/2) < π(x) for x ≥ 67 (2) x/(log x - 3/2) > π(x) for $x > e^{3 / 2}$ . The proof of the above inequalities is not elementary and is based on the first 25 000 zeros of the Riemann function ξ(s) obtained by D. H. Lehmer [4]. Then Rosser, Yohe...

A $ℤ^{d}$ generalization of the Davenport-Erdős construction of normal numbers

Mordechay Levin, Meir Smorodinsky (2000)

Colloquium Mathematicae

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We extend the Davenport and Erdős construction of normal numbers to the $ℤ^{d}$ case.

Displaying similar documents to “On the number of representations in the Waring-Goldbach problem with a prime variable in an arithmetic progression”

On the parity of generalized partition functions, III

An arithmetic formula of Liouville

Factorization problems in class number two

CM liftings of supersingular elliptic curves

A combinatorial identity arising from cobordism theory.

Inequalities concerning the function π(x): Applications

A ℤ d generalization of the Davenport-Erdős construction of normal numbers

A $ℤ^{d}$ generalization of the Davenport-Erdős construction of normal numbers