The distribution and moments of the error term in the Dirichlet divisor problem

D. R. Heath-Brown

Acta Arithmetica (1992)

  • Volume: 60, Issue: 4, page 389-415
  • ISSN: 0065-1036

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D. 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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  1. [1] F. V. Atkinson, A divisor problem, Quart. J. Math. Oxford Ser. 12 (1941), 193-200. Zbl0063.00134
  2. [2] F. V. Atkinson, The mean-value of the Riemann zeta function, Acta Math. 81 (1949), 353-376. Zbl0036.18603
  3. [3] H. Cramér, Über zwei Sätze von Herrn G. H. Hardy, Math. Z. 15 (1922), 201-210. 
  4. [4] D. R. Heath-Brown, The mean value theorem for the Riemann zeta-function, Mathematika 25 (1978), 177-184. Zbl0387.10023
  5. [5] D. R. Heath-Brown and M. N. Huxley, Exponential sums with a difference, Proc. London Math. Soc. (3) 61 (1990), 227-250. Zbl0675.10027
  6. [6] A. Ivić, The Riemann Zeta-function, Wiley, New York 1985. Zbl0556.10026
  7. [7] H. Iwaniec and C. J. Mozzochi, On the divisor and circle problems, J. Number Theory 29 (1988), 60-93. Zbl0644.10031
  8. [8] K.-L. Kueh, The moments of infinite series, J. Reine Angew. Math. 385 (1988), 1-9. 
  9. [9] E. C. Titchmarsh, The Theory of the Riemann Zeta-function, 2nd ed., Oxford Univ. Press, Oxford 1986. Zbl0601.10026
  10. [10] K.-C. Tong, On divisor problems, III, Acta Math. Sinica 6 (1956), 515-541. Zbl0075.25003
  11. [11] K.-M. Tsang, Higher power moments of Δ(x), E(t) and P(x), Proc. London Math. Soc. (3), to appear. 
  12. [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

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  1. Aleksandar Ivić, On some problems involving Hardy’s function
  2. Pavel M. Bleher, Freeman J. Dyson, Mean square value of exponential sums related to representation of integers as sum of two squares
  3. Aleksandar Ivić, On the riemann zeta-function and the divisor problem
  4. Manfred Kühleitner, Werner Nowak, On differences of two squares
  5. Aleksandar Ivić, Power moments of the error term in the approximate functional equation for ζ²(s)
  6. Pavel M. Bleher, Freeman J. Dyson, Mean square limit for lattice points in a sphere
  7. 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 3 / 4 σ &lt; 1

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