4 problems

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Goldmakher's conjecture on logarithmic sums of multiplicative functions
Goldmakher's conjecture. Let $f\in\mathcal{F}$ . Then for any $1\leq y\leq x$ ,
Conjecturesolvedanalytic-number-theory multiplicative-functions pretentious-number-theoryarXiv posted 2 days ago
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Hardy–Littlewood–Elliott conjecture
Hardy–Littlewood–Elliott conjecture. Then
Conjectureopenmultiplicative-functions pretentious-number-theory prime-correlationsarXiv posted 2 days ago
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The bounded-distance characterization of mock characters
Bounded-distance conjecture. For any mock character $\kappa$ , there exists a Dirichlet character $\chi$ such that $\mathbb D(\kappa,\chi;y)$ is bounded. Conversely, if…
Conjectureopenautomatic-sequences mock-characters pretentious-number-theoryarXiv posted 2 days ago
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The constant-function mimicry conjecture for weighted multiplicative sums
Constant-function mimicry conjecture. One has
Conjectureopencharacter-sums multiplicative-functions pretentious-number-theoryarXiv posted 2 days ago

Goldmakher's conjecture on logarithmic sums of multiplicative functions