The Generalized Polynomial Goldbach Problem
نویسندگان
چکیده
منابع مشابه
The exceptional set in the polynomial Goldbach problem
For each natural number N , let R(N) denote the number of representations of N as a sum of two primes. Hardy and Littlewood proposed a plausible asymptotic formula for R(2N) and showed, under the assumption of the Riemann Hypothesis for Dirichlet Lfunctions, that the formula holds “on average” in a certain sense. From this they deduced (under ERH) that all but O (x1/2+ ) of the even natural num...
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Leonhard Euler (1707–1783) – one of the greatest mathematicians of the eighteenth century and of all times – often corresponded with a friend of his, Christian Goldbach (1690–1764), an amateur and poly-math who lived and worked in Russia, just like Euler himself. In a letter written in June 1742, Goldbach made a conjecture – that is, an educated guess – on prime numbers: Es scheinet wenigstens,...
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David Hayes observed in 1965 that when R = Z, every element of R[T ] of degree n ≥ 1 is a sum of two irreducibles in R[T ] of degree n. We show that this result continues to hold for any Noetherian domain R with infinitely many maximal ideals. It appears that David Hayes [5] was the first to observe the following polynomial analogue of the celebrated Goldbach conjecture: If R = Z, then (?) ever...
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The two conjectures are, of course, equivalent. If 2n — 2 = pi+p2, then 2n = pi+p2+2 and 2n + l = pi+p2+3Conversely, if 2n=pi -\-p2-\-pz one of the primes must be 2 and 2n — 2 = pi+p2. An impressive collection of numerical evidence indicating the truth of the conjectures has accumulated in the years since Goldbach's letter was written, but is it not known to this day whether the conjectures are...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1996
ISSN: 0022-314X
DOI: 10.1006/jnth.1996.0032