The distribution and moments of the error term in the Dirichlet divisor problem
Acta Arithmetica (1992)
- Volume: 60, Issue: 4, page 389-415
- ISSN: 0065-1036
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topD. R. Heath-Brown. "The distribution and moments of the error term in the Dirichlet divisor problem." Acta Arithmetica 60.4 (1992): 389-415. <http://eudml.org/doc/206446>.
@article{D1992,
author = {D. R. Heath-Brown},
journal = {Acta Arithmetica},
keywords = {Riemann zeta function; error term; Dirichlet divisor problem; distribution function; moments; circle problem; Piltz divisor problem; asymptotic formula; mean square},
language = {eng},
number = {4},
pages = {389-415},
title = {The distribution and moments of the error term in the Dirichlet divisor problem},
url = {http://eudml.org/doc/206446},
volume = {60},
year = {1992},
}
TY - JOUR
AU - D. R. Heath-Brown
TI - The distribution and moments of the error term in the Dirichlet divisor problem
JO - Acta Arithmetica
PY - 1992
VL - 60
IS - 4
SP - 389
EP - 415
LA - eng
KW - Riemann zeta function; error term; Dirichlet divisor problem; distribution function; moments; circle problem; Piltz divisor problem; asymptotic formula; mean square
UR - http://eudml.org/doc/206446
ER -
References
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- [6] A. Ivić, The Riemann Zeta-function, Wiley, New York 1985. Zbl0556.10026
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- [8] K.-L. Kueh, The moments of infinite series, J. Reine Angew. Math. 385 (1988), 1-9.
- [9] E. C. Titchmarsh, The Theory of the Riemann Zeta-function, 2nd ed., Oxford Univ. Press, Oxford 1986. Zbl0601.10026
- [10] K.-C. Tong, On divisor problems, III, Acta Math. Sinica 6 (1956), 515-541. Zbl0075.25003
- [11] K.-M. Tsang, Higher power moments of Δ(x), E(t) and P(x), Proc. London Math. Soc. (3), to appear.
- [12] G. Voronoï, Sur une fonction transcendante et ses applications à la sommation de quelques séries, Ann. Sci. École Norm. Sup. (3) 21 (1904), 207-267 & 459-533. Zbl35.0220.01
Citations in EuDML Documents
top- Aleksandar Ivić, On some problems involving Hardy’s function
- Pavel M. Bleher, Freeman J. Dyson, Mean square value of exponential sums related to representation of integers as sum of two squares
- Aleksandar Ivić, On the riemann zeta-function and the divisor problem
- Manfred Kühleitner, Werner Nowak, On differences of two squares
- Aleksandar Ivić, Power moments of the error term in the approximate functional equation for ζ²(s)
- Pavel M. Bleher, Freeman J. Dyson, Mean square limit for lattice points in a sphere
- Yuk-Kam Lau, A study of the mean value of the error term in the mean square formula of the Riemann zeta-function in the critical strip
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