Results 1 to 10 of about 24,999 (231)
On Gaps Between Primitive Roots in the Hamming Metric [PDF]
, 2012 We consider a modification of the classical number theoretic question about the gaps between consecutive primitive roots modulo a prime $p$, which by the well-known result of Burgess are known to be at most $p^{1/4+o(1)}$. Here we measure the distance in
Dietmann, Rainer +2 more
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Quantitative relations between short intervals and exceptional sets of cubic Waring-Goldbach problem
Open Mathematics, 2017 In this paper, we are able to prove that almost all integers n satisfying some necessary congruence conditions are the sum of j almost equal prime cubes with j = 7, 8, i.e., N=p13+…+pj3$\begin{array}{} N=p_1^3+ \ldots +p_j^3 \end{array} $ with |pi−(N ...
Feng Zhao
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Average bounds for Kloosterman sums over primes [PDF]
Functiones et Approximatio Commentarii Mathematici, 2014 We prove two estimates for averages of sums of Kloosterman fractions over primes. The first of these improves previous results of Fouvry-Shparlinski and Baker.
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Exponential Sums Over Primes in an Arithmetic Progression [PDF]
Proceedings of the American Mathematical Society, 1985 In 1979 A. F. Lavrik obtained some estimates for exponential sums over primes in arithmetic progressions by an analytic method. In the present paper we give an estimate for the same sums, comparable with Lavrik’s estimate, by means of elementary methods like Vaughan’s identity.
A. BALOG, PERELLI, ALBERTO
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On Sums of Powers of Almost Equal Primes [PDF]
, 2014 We investigate the Waring-Goldbach problem of representing a positive integer $n$ as the sum of $s$ $k$th powers of almost equal prime numbers. Define $s_k=2k(k-1)$ when $k\ge 3$, and put $s_2=6$.
Wei, Bin, Wooley, Trevor D.
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Sign changes of Kloosterman sums with almost prime moduli [PDF]
, 2014 We prove that the Kloosterman sum $S(1,1;c)$ can change sign infinitely often as $c$ runs over squarefree moduli with at most 10 prime factors, which improves the previous results of E. Fouvry and Ph. Michel, J. Sivak-Fischler and K.
Xi, Ping
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Primes in short arithmetic progressions
, 2003 We give a large sieve type inequality for functions supported on primes. As application we prove a conjecture by Elliott, and give bounds for short character sums over primes.
Schlage-Puchta, Jan-Christoph
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On certain sums over primes and the Riesz function
Математичні СтудіїWe offer some comments on series involving the M$\ddot{o}$bius function which approximate sums over primes. To accomplish this, we utilize the derivative of the Gram series by applying Riemann-Stieltjes integration.
Alexander Patkowski
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Mean values of Dirichlet polynomials and applications to linear equations with prime variables
, 2004 We prove a new mean-value theorem for Dirichlet polynomials with coefficients given by the von Mangoldt function. We then use our theorem to derive new estimates for certain exponential sums over primes.
Angel V. Kumchev +2 more
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New proof and generalization of some results on translated sums over k-almost primes
Comptes Rendus. MathématiqueA sequence $\mathcal{A}$ of strictly positive integers is said to be primitive if none of its terms divides the others, Erdős conjectured that the sum $f(\mathcal{A},0)\le f(\mathbb{N}_{1},0),$ where $\mathbb{N}_{1}$ is the sequence of prime numbers and $
Laib, Ilias
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