Results 101 to 110 of about 5,332 (130)

Linear support for the prime number sequence and the first and second Hardy-Littlewood conjectures

MATHEMATICA SCANDINAVICA
Servais and Grün used results about linear support for the prime number sequence to obtain upper bounds on the smallest prime in odd perfect numbers. This was extended by Cohen and Hendy who proved that for every $n \in \mathbb {N}$ there exists an integer $b_n$ such that $p_i \ge p_1 + ni - b_n$ for any sequence $(p_i)$ of odd primes, and found ...
Aslaksen, Helmer, Kirfel, Christoph
openaire   +2 more sources

A Spectral-Fractal Proof of the Hardy-Littlewood Conjecture

We present a complete spectral-fractal proof of the first Hardy-Littlewood conjecture concerning the asymptotic distribution of twin primes. The conjecture asserts that the number of twin prime pairs (p, p + 2) up to N is asymptotically equivalent to 2C2 R N2dt (log t)2 , where C2 = Q p>2(1− 1 (p−1)2 ) is the twin prime constant, implying their ...
openaire   +1 more source

Reinterpreting the Hardy–Littlewood Prime Pair Conjecture through ParityScript: A Framework of Resonance, Duality, and Informational Harmonics

This work reinterprets the Hardy–Littlewood Prime Pair Conjecture through the ParityScript framework, a formal system that encodes primes as ruptures in the parity lattice and prime pairs as dual resonances connected by resonance spans. The Hardy–Littlewood correction factor is reframed as a resonance intensity operator, quantifying informational ...
Rezapour, Majid, Rezapour, Ramin
openaire   +1 more source

Enveloping sieve related to the Hardy-Littlewood irreducible tuple conjecture in a function field

Finite Fields and Their Applications
Let \(\mathbb{A}=\mathbb{F}_q(t)\) be the polynomial ring over the finite field \(\mathbb{F}_q\) of \(q\) elements. Let \(l\in \mathbb{N }_+=\{1,2,\ldots\}\), \(\{a_1,\ldots,a_l\}\subset\mathbb{A}\setminus{\{0\}}\), \(\{\widehat{a}_1,\ldots,\widehat{a}_l\}\subset\mathbb{A}\), and \[ H(x)=\prod_{j=1}^{l}\big(a_j x+\widehat{a}_j\big). \] In addition, let
openaire   +1 more source

Final Proof of the Goldbach Conjecture: Hardy-Littlewood Circle Method with Exponential Sums

A Complete Analytic Proof of the Goldbach Conjecture Using Circle Method and Sieve Theory This paper presents a full resolution of the Goldbach Conjecture, proving that every even integer greater than 2 is the sum of two prime numbers. The proof integrates classical and modern techniques from analytic number theory to construct a seamless argument ...
openaire   +1 more source

An Intuitive Reformulation of the Hardy-Littlewood Prime Tuple Conjecture Through Adolescent Insight

This paper presents novel intuitive perspectives on the Hardy-Littlewood Prime Tuple Conjecture developed by a 16-year-old student.Through discontinuous but intense 9-hour focus, I developedunderstanding of advanced number theory concepts and propose pedagogicalreformulations that make these ideas accessible to youngerstudents and non-specialists.
openaire   +1 more source

The Mazur Conjecture, the Lang-Trotter Conjecture and the Hardy-Littlewood Conjecture

2022
openaire   +1 more source

Hardy spaces with variable exponents and generalized Campanato spaces

Journal of Functional Analysis, 2012
Eiichi Nakai, Yoshihiro Sawano
exaly  

Non-linear ground state representations and sharp Hardy inequalities

Journal of Functional Analysis, 2008
Rupert L Frank, Robert Seiringer
exaly  

Hardy-Weinberg Equilibrium Testing of Biological Ascertainment for Mendelian Randomization Studies

American Journal of Epidemiology, 2009
Santiago Rodriguez, Tom R Gaunt
exaly