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A separation property of the zeros of Eisenstein series for SL(2, ℤ)
Author(s) -
Nozaki Hiroshi
Publication year - 2008
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/blms/bdm117
Subject(s) - mathematics , series (stratigraphy) , eisenstein series , property (philosophy) , separation (statistics) , pure mathematics , statistics , epistemology , modular form , paleontology , philosophy , biology
Let E k ( z ) be the Eisenstein series with weight k for the modular group SL(2, ℤ). We prove that the zeros of E k ( e iθ ) interlace with the zeros of E k +12 ( e iθ ) on π /2 < θ < 2 π /3. That is, any zero of E k ( e iθ ) lies between two consecutive zeros of E k +12 ( e iθ ) on π /2 < θ < 2 π /3.