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On an extremal property of the Rudin‐Shapiro sequence
Author(s) -
Allouche Jean-Paul,
France Michel Mendès
Publication year - 1985
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300010822
Subject(s) - mathematics , unimodular matrix , multiplicative function , sequence (biology) , property (philosophy) , combinatorics , mathematical analysis , philosophy , genetics , epistemology , biology
Extending the well‐known property of the Rudin‐ Shapiro sequence ε = (ε(n)) with values in {−1, +1} satisfyingsup 0 ⩽ θ ⩽ 2 π|∑ n = 0 N − 1ε ( n ) exp ( 2 i π n θ )| ⩽ ( 2 + √ 2 ) √ N ,we show that for all unimodular 2‐multiplicative sequences f = (f(n))|∑ n = 0 N − 1ε ( n ) f ( n )| ⩽ ( 2 + √ 2 ) √ N .