Lines full of Dedekind sums

G. Myerson; N. Phillips

doi:10.1112/S0024609304003133

Lines full of Dedekind sums

G. Myerson, N. Phillips

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Let s: ℚ → ℚ be the Dedekind sum, given by s(h/k) = ∑_v=1 ^k-1(v/k-1/2)({hv/k} - 1/2) when gcd (h, k) = 1. Then for every rational α ≠ 1/12 there are infinitely many rational x such that s(x) = αx. Also, the fixed points of s are dense in the real line.

Original language	English
Pages (from-to)	547-552
Number of pages	6
Journal	Bulletin of the London Mathematical Society
Volume	36
Issue number	4
DOIs	https://doi.org/10.1112/S0024609304003133
Publication status	Published - Jul 2004

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title = "Lines full of Dedekind sums",

abstract = "Let s: ℚ → ℚ be the Dedekind sum, given by s(h/k) = ∑v=1 k-1(v/k-1/2)({hv/k} - 1/2) when gcd (h, k) = 1. Then for every rational α ≠ 1/12 there are infinitely many rational x such that s(x) = αx. Also, the fixed points of s are dense in the real line.",

author = "G. Myerson and N. Phillips",

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AU - Myerson, G.

AU - Phillips, N.

PY - 2004/7

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N2 - Let s: ℚ → ℚ be the Dedekind sum, given by s(h/k) = ∑v=1 k-1(v/k-1/2)({hv/k} - 1/2) when gcd (h, k) = 1. Then for every rational α ≠ 1/12 there are infinitely many rational x such that s(x) = αx. Also, the fixed points of s are dense in the real line.

AB - Let s: ℚ → ℚ be the Dedekind sum, given by s(h/k) = ∑v=1 k-1(v/k-1/2)({hv/k} - 1/2) when gcd (h, k) = 1. Then for every rational α ≠ 1/12 there are infinitely many rational x such that s(x) = αx. Also, the fixed points of s are dense in the real line.

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DO - 10.1112/S0024609304003133

M3 - Article

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VL - 36

SP - 547

EP - 552

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 4

ER -

Lines full of Dedekind sums

Abstract

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