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Mean values of finite Euler products
Author(s) -
Gonek S. M.,
Keating J. P.
Publication year - 2010
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdq049
Subject(s) - mathematics , euler's formula , modulus , moduli , product (mathematics) , mathematical analysis , plane (geometry) , square (algebra) , geometry , physics , quantum mechanics
We prove several theorems concerning mean values of the modulus squared of finite Euler products in right half‐planes of the complex plane. We are particularly interested in knowing when the mean of the modulus squared of the Euler product is asymptotic to the product of the mean moduli squared of the individual Euler factors. That is, when the factors are ‘independent’.