Jia's strengthened Hardy–Littlewood conjecture for Goldbach representations
Jia's strengthened Hardy–Littlewood conjecture for Goldbach representations
Let denote the number of representations of an integer as a sum of two primes, and let denote Euler's totient function. Jia's strengthened Hardy–Littlewood conjecture. Suppose that is sufficiently large and . There exists an absolute constant such that, for the even integers satisfying and ,
The source presents this as a stronger version of the weak Hardy–Littlewood conjecture and attributes its use in bounding Siegel zeros to Jia; the assertion itself remains unproved.
Sources & referencesView supporting material
Primary source
Yunan Wang, “Siegel Zeros and the Hardy-Littlewood Conjecture”, arXiv:2402.19332 (2024).
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