# An explicit formula of Atkinson type for the product of the Riemann zeta-function and a Dirichlet polynomial

Hideaki Ishikawa; Kohji Matsumoto

Open Mathematics (2011)

- Volume: 9, Issue: 1, page 102-126
- ISSN: 2391-5455

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topHideaki Ishikawa, and Kohji Matsumoto. "An explicit formula of Atkinson type for the product of the Riemann zeta-function and a Dirichlet polynomial." Open Mathematics 9.1 (2011): 102-126. <http://eudml.org/doc/269380>.

@article{HideakiIshikawa2011,

abstract = {We prove an explicit formula of Atkinson type for the error term in the asymptotic formula for the mean square of the product of the Riemann zeta-function and a Dirichlet polynomial. To deal with the case when coefficients of the Dirichlet polynomial are complex, we apply the idea of the first author in his study on mean values of Dirichlet L-functions.},

author = {Hideaki Ishikawa, Kohji Matsumoto},

journal = {Open Mathematics},

keywords = {Riemann zeta-function; Dirichlet polynomial; Atkinson formula},

language = {eng},

number = {1},

pages = {102-126},

title = {An explicit formula of Atkinson type for the product of the Riemann zeta-function and a Dirichlet polynomial},

url = {http://eudml.org/doc/269380},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Hideaki Ishikawa

AU - Kohji Matsumoto

TI - An explicit formula of Atkinson type for the product of the Riemann zeta-function and a Dirichlet polynomial

JO - Open Mathematics

PY - 2011

VL - 9

IS - 1

SP - 102

EP - 126

AB - We prove an explicit formula of Atkinson type for the error term in the asymptotic formula for the mean square of the product of the Riemann zeta-function and a Dirichlet polynomial. To deal with the case when coefficients of the Dirichlet polynomial are complex, we apply the idea of the first author in his study on mean values of Dirichlet L-functions.

LA - eng

KW - Riemann zeta-function; Dirichlet polynomial; Atkinson formula

UR - http://eudml.org/doc/269380

ER -

## References

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