Results 61 to 70 of about 5,332 (130)

Consecutive Piatetski-Shapiro primes based on the Hardy-Littlewood conjecture

Journal of Number Theory
We add a new section also with more data analysis.
Guo, Victor Zhenyu, Yi, Yuan
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The Hardy-Littlewood Prime K-Tuple Conjecture Is False

The Journal of Middle East and North Africa Sciences, 2016
Using Jiang function we prove Jiang prime k -tuple theorem. We prove that the Hardy-Littlewood prime k -tuple conjecture is false. Jiang prime k -tuple theorem can replace the Hardy-Littlewood prime k -tuple conjecture. (A) Jiang prime k -tuple theorem [1, 2]. We define the prime k -tuple equation , i p p n + , (1) where 2 , 1, 1 i n i k = − L .
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The approximate functional equation of some Diophantine series. [PDF]

Mon Hefte Math, 2023
Chamizo F, Martin B.
europepmc   +1 more source

Generalising the Hardy-Littlewood Method for Primes

, 2006
The Hardy-Littlewood method is a well-known technique in analytic number theory. Among its spectacular applications are Vinogradov's 1937 result that every sufficiently large odd number is a sum of three primes, and a related result of Chowla and Van der
Green, Ben
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Simple Proof of the Hardy–littlewood Conjecture

Annals of Mathematics and Physics
The Hardy–Littlewood conjecture suggests that every odd integer 2n + 1 greater than or equal to 7 is the sum of three prime numbers, two of which are equal. In this paper, we present a simple approach that attempts to prove this conjecture.
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Hardy-Littlewood tuple conjecture over large finite field

, 2012
minor ...
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Extreme values of derivatives of the Riemann zeta function. [PDF]

Mathematika, 2022
Yang D.
europepmc   +1 more source

Applying Discrete Fourier Transform to the Hardy-Littlewood Conjecture

, 2016
We study the asymptotic behaviour of the prime pair counting function $ _{2k}(n)$ by the means of the discrete Fourier transform on $\mathbb{Z}/ n\mathbb{Z}$. The method we develop can be viewed as a discrete analog of the Hardy-Littlewood circle method.
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Sums of integer cubes. [PDF]

Proc Natl Acad Sci U S A, 2021
Siksek S.
europepmc   +1 more source

A fractional version of Rivière's GL(n)-gauge. [PDF]

Ann Mat Pura Appl, 2022
Da Lio F, Mazowiecka K, Schikorra A.
europepmc   +1 more source