Skip to content

Erdős problem 975

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?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/975.lean

Formal Conjectures

FormalConjectures/ErdosProblems/975.leanErdos975.erdos_9756 linesExact file
True ↔  ∀ (f : Polynomial ℤ),    f.natDegree ≠ 0 →      Irreducible f →        (∀ᶠ (n : ℤ) in Filter.atTop, 1 ≤ Polynomial.eval n f) →          ∃ c > 0, Filter.Tendsto (fun x => Erdos975.Erdos975Sum f x / (x * Real.log x)) Filter.atTop (nhds c)
OpenStatement only, no proof

Continue

Start a contributionBrowse the source filesOpen the collection entry

Search problems.science

Find a Problem, Result, source, or page