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Erdős problem 975

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For an irreducible polynomial f∈Z[x]f \in \mathbb{Z}[x] with f(n)≥1f(n) \ge 1 for sufficiently large nn, does there exists a constant c=c(f)>0c = c(f) > 0 such that ∑n≤xτ(f(n))≈c⋅xlog⁡x\sum_{n \le x} \tau(f(n)) \approx c \cdot x \log x?

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6 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

975.lean

Retained formal statement2 of 6

Lower bound for the growth rate of Erdos975Sum, shown in [Va39].

FormalConjectures/ErdosProblems/975.leanErdos975.erdos_975.variants.lower_bound5 linesExact file
∀ (f : Polynomial ℤ),  Irreducible f →    f.natDegree ≠ 0 →      (∀ᶠ (n : ℤ) in Filter.atTop, 1 ≤ Polynomial.eval n f) →        (fun x => x * Real.log x) =O[Filter.atTop] Erdos975.Erdos975Sum f
SolvedStatement only, no proof