Formulas for the number of gridlines

DOI10.1007/s00605-010-0236-6zbMath1250.05023OpenAlexW2041974468WikidataQ60691952 ScholiaQ60691952MaRDI QIDQ646615

Pentti Haukkanen, Anne-Maria Ernvall-Hytönen, Jorma Kaarlo Merikoski, Kaisa Matomäki

Publication date: 17 November 2011

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-010-0236-6

zbMATH Keywords

lattice pointsasymptotic formulasrectangular gridrecursive formulasEuler \(\phi\)-function

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Asymptotic results on arithmetic functions (11N37) Recurrences (11B37) Lattice points in specified regions (11P21)

Related Items

ASYMPTOTICS FOR NUMBERS OF LINE SEGMENTS AND LINES IN A SQUARE GRID

Uses Software

• OEIS

Cites Work

• A note on Euler's phi-function
• On an estimate of Walfisz and Saltykov for an error term related to the Euler function
• On the average order of the function \(E(x) = \sum_{n\leq x}\varphi(n)-{{3x^ 2}\over{\pi^ 2}}\).
• Pizza Slicing, Phi's and the Riemann Hypothesis
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