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Application to Dirichlet Series of Maximal Large Sieve Inequality
Author(s) -
Long Ruilin,
Liu Zhengquan
Publication year - 1993
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/25.2.105
Subject(s) - mathematics , sieve (category theory) , combinatorics , dirichlet series , series (stratigraphy) , measure (data warehouse) , dirichlet distribution , pure mathematics , mathematical analysis , paleontology , database , computer science , boundary value problem , biology
In this note, the maximal Large Sieve inequality has been used to obtain following estimate: '∫ ‐ T Tsup| D ( S ) | 2 d μ ( t ) ⩽ Cσ ⩾ 0supτ∫ U + τd μ ( t )| U |‐ 1∑ 1 N ( T + n ) |a n|2where D ( s )= ∑ 1 Na n n ‐ s, s =σ+ it , is a Dirichlet series, d μ is a nonnegative Borel measure on R and U = [− C log − 1 N ] (say T ⩾1). In addition, the higher‐dimensional version of (*) has been obtained.
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