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Lines Full of Dedekind Sums
Author(s) -
Myerso G.,
Phillips N.
Publication year - 2004
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609304003133
Subject(s) - mathematics , dedekind cut , dedekind sum , line (geometry) , mathematics subject classification , real line , combinatorics , dedekind eta function , rational number , discrete mathematics , pure mathematics , modular form , geometry , eisenstein series
Let s : Q→Q be the Dedekind sum, given by∑ v = 1 k − 1( v / k − 1 / 2 ) ( { h v / 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 )=α x . Also, the fixed points of s are dense in the real line. 2000 Mathematics Subject Classification 11F20.