Handbuch der Lehre von der Verteilung der Primzahlen¶
Landau, E. (1909). Handbuch der Lehre von der Verteilung der Primzahlen.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Complexity (Time/Space)
- The asymptotic growth-rate function (O, Ω, Θ notation expressing input-size dependence)
This sourceTeubner. Source of the modern big-O / little-o (Landau-symbol) asymptotic notation used to express growth-rate / input-size dependence — supports D30-136. Verified existing and supporting.
Supported in partVerified against the work's full text
Landau introduces the O and o symbols and "same order of magnitude" for asymptotic comparison of functions as x tends to infinity; Omega and Theta notation and input-size/complexity use are absent.
“Dies Zeichen 0 gestattet oftmals bei komplizierten Formeln”
- The asymptotic growth-rate function (O, Ω, Θ notation expressing input-size dependence)
Domain-specific¶
- Big O Notation
- Algorithm analysis — the heaviest-used habitat: stating worst-case (or average- or best-case) running time and space in input size, via the compositional algebra (O(f)+O(g)=O(max(f,g)), nested loops as O(f·g)). Computational complexity theory — the complexity classes (P, NP, PSPACE, EXPTIME) are defined by the asymptotic resource bounds their problems respect, so tractability is read as a question of growth class. Analytic number theory — the notation's birthplace under Bachmann and Landau: bounding error terms in prime-counting and the growth of arithmetic functions
Supported in partVerified against the work's full text
“prime-number theorem and the prime-number theorem for [arithmetic] progressions as such (without any estimation”
- Algorithm analysis — the heaviest-used habitat: stating worst-case (or average- or best-case) running time and space in input size, via the compositional algebra (O(f)+O(g)=O(max(f,g)), nested loops as O(f·g)). Computational complexity theory — the complexity classes (P, NP, PSPACE, EXPTIME) are defined by the asymptotic resource bounds their problems respect, so tractability is read as a question of growth class. Analytic number theory — the notation's birthplace under Bachmann and Landau: bounding error terms in prime-counting and the growth of arithmetic functions
Verification¶
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