Mean square of the remainder term in the Dirichlet divisor problem

Yuk-Kam Lau; Kai-Man Tsang

Journal de théorie des nombres de Bordeaux (1995)

  • Volume: 7, Issue: 1, page 75-92
  • ISSN: 1246-7405

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Lau, Yuk-Kam, and Tsang, Kai-Man. "Mean square of the remainder term in the Dirichlet divisor problem." Journal de théorie des nombres de Bordeaux 7.1 (1995): 75-92. <http://eudml.org/doc/247656>.

@article{Lau1995,
author = {Lau, Yuk-Kam, Tsang, Kai-Man},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {mean square; error term; Dirichlet divisor problem},
language = {eng},
number = {1},
pages = {75-92},
publisher = {Université Bordeaux I},
title = {Mean square of the remainder term in the Dirichlet divisor problem},
url = {http://eudml.org/doc/247656},
volume = {7},
year = {1995},
}

TY - JOUR
AU - Lau, Yuk-Kam
AU - Tsang, Kai-Man
TI - Mean square of the remainder term in the Dirichlet divisor problem
JO - Journal de théorie des nombres de Bordeaux
PY - 1995
PB - Université Bordeaux I
VL - 7
IS - 1
SP - 75
EP - 92
LA - eng
KW - mean square; error term; Dirichlet divisor problem
UR - http://eudml.org/doc/247656
ER -

References

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  1. [1] D.R. Heath-Brown, The fourth power moment of the Riemann zeta-function, Proc. London Math. Soc.38 (3) (1979), 385-422. Zbl0403.10018MR532980
  2. [2] D.R. Heath-Brown and K.M. Tsang, Sign changes of E(T), Δ(x) and P(x), J. Number Theory49 (1994), 73-83. Zbl0810.11046
  3. [3] A. Ivić, The Riemann zeta-function, Wiley, New York-Brisbane- Singapore1985. Zbl0556.10026MR792089
  4. [4] A. Ivić, Lectures on mean values of the Riemann zeta-function, Springer Verlag, Berlin- Heidelberg-New York-Tokyo, 1991. Zbl0758.11036MR1230387
  5. [5] H. Iwaniec and C.J. Mozzochi, On the divisor and circle problems, J. Number Theory29 (1988), 60-93. Zbl0644.10031MR938870
  6. [6] T. Meurman, On the mean square of the Riemann zeta-function, Quart. J. Math. (Oxford) (2)38, (1987), 337-343. Zbl0624.10032MR907241
  7. [7] E. Preissmann, Sur la moyenne quadratique du terme de reste du problème du cercle, C.R. Acad. Sci. Paris Sér. I306 (1988), 151-154. Zbl0654.10042MR930552
  8. [8] E.C. Titchmarsh, The theory of the Riemann zeta-function, (2nd ed. revised by D.R. HEATH-BROWN), Clarendon Press, Oxford, 1986. Zbl0601.10026MR882550
  9. [9] K.C. Tong, On divisor problems I, Acta Math. Sinica5, no.3 (1955), 313-324. Zbl0068.26804MR73632
  10. [10] K.C. Tong, On divisor problems III, Acta Math. Sinica6, no.4 (1956), 515-541. Zbl0075.25003MR98718
  11. [11] K. Tsang, A mean value theorem in the dirichlet divisor problem, preprint. 
  12. [12] G.F. Voronoi, Sur une fonction transcendante et ses applications à la sommation de quelques séries, Ann. École Normale21(3) (1904), 207-268; 459-534. JFM35.0220.01
  13. [13] G.N. Watson, A treatise on the theory of Bessel functions, 2nd edition, Cambridge University Press, 1962. Zbl0174.36202

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