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The Mean Square of the Error Term for the Fourth Power Moment of the Zeta‐Function
Author(s) -
Ivić Aleksandar,
Motohashi Yoichi
Publication year - 1994
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-69.2.309
Subject(s) - mathematics , asymptotic formula , term (time) , riemann zeta function , divisor (algebraic geometry) , divisor function , moment (physics) , combinatorics , square (algebra) , function (biology) , binary number , pure mathematics , arithmetic , geometry , physics , classical mechanics , quantum mechanics , evolutionary biology , biology
We prove that ∫ 0 τE 2( t ) 2 d t ≪ T 2log C T , where E 2 ( T ) denotes the error term in the asymptotic formula for ∫ 0 τ | ζ ( 1 2 + i t ) | 4 d t ; the proof depends on the second author's explicit formula for a modified version of the latter integral. Several related results are also proved, including the analogue of the above result for the binary additive divisor problem.