Power moments of the error term in the approximate functional equation for ζ²(s)

Aleksandar Ivić

Acta Arithmetica (1993)

  • Volume: 65, Issue: 2, page 137-145
  • ISSN: 0065-1036

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Aleksandar Ivić. "Power moments of the error term in the approximate functional equation for ζ²(s)." Acta Arithmetica 65.2 (1993): 137-145. <http://eudml.org/doc/206566>.

@article{AleksandarIvić1993,
author = {Aleksandar Ivić},
journal = {Acta Arithmetica},
keywords = {Riemann zeta-function; approximate functional equation; Voronoï formula for the divisor problem; d(n) the number of divisors of n; Voronoi formula for the divisor problem; error term; evaluation of power moments},
language = {eng},
number = {2},
pages = {137-145},
title = {Power moments of the error term in the approximate functional equation for ζ²(s)},
url = {http://eudml.org/doc/206566},
volume = {65},
year = {1993},
}

TY - JOUR
AU - Aleksandar Ivić
TI - Power moments of the error term in the approximate functional equation for ζ²(s)
JO - Acta Arithmetica
PY - 1993
VL - 65
IS - 2
SP - 137
EP - 145
LA - eng
KW - Riemann zeta-function; approximate functional equation; Voronoï formula for the divisor problem; d(n) the number of divisors of n; Voronoi formula for the divisor problem; error term; evaluation of power moments
UR - http://eudml.org/doc/206566
ER -

References

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  1. [1] D. R. Heath-Brown, The distribution and moments of the error term in the Dirichlet divisor problem, Acta Arith. 60 (1992), 389-415. Zbl0725.11045
  2. [2] A. Ivić, Large values of the error term in the divisor problem, Invent. Math. 71 (1983), 513-520. Zbl0489.10045
  3. [3] A. Ivić, The Riemann Zeta-function, Wiley, New York, 1985. Zbl0556.10026
  4. [4] A. Ivić, Large values of certain number-theoretic error terms, Acta Arith. 56 (1990), 135-159. Zbl0659.10053
  5. [5] H. Iwaniec and C. J. Mozzochi, On the divisor and circle problems, J. Number Theory 29 (1988), 60-93. Zbl0644.10031
  6. [6] I. Kiuchi, An improvement on the mean value formula for the approximate functional equation of the square of the Riemann zeta-function, J. Number Theory, to appear. Zbl0787.11034
  7. [7] I. Kiuchi, Power moments of the error term for the approximate functional equation of the Riemann zeta-function, Publ. Inst. Math. (Beograd) 52 (66) (1992), in print. Zbl0793.11021
  8. [8] I. Kiuchi and K. Matsumoto, Mean value results for the approximate functional equation of the square of the Riemann zeta-function, Acta Arith. 61 (1992), 337-345. Zbl0761.11035
  9. [9] T. Meurman, On the mean square of the Riemann zeta-function, Quart. J. Math. Oxford Ser. (2) 38 (1987), 337-343. Zbl0624.10032
  10. [10] Y. Motohashi, A note on the approximate functional equation for ζ²(s), Proc. Japan Acad. Ser. A 59 (1983), 393-396 and II, Quart. J. Math. Oxford Ser. 469-472. 
  11. [11] Y. Motohashi, Lectures on the Riemann-Siegel Formula, Ulam Seminar, Dept. Math., Colorado University, Boulder, 1987. 
  12. [12] E. Preissmann, Sur la moyenne quadratique du terme de reste du problème du cercle, C. R. Acad. Sci. Paris 306 (1988), 151-154. Zbl0654.10042
  13. [13] K.-C. Tong, On divisor problem III, Acta Math. Sinica 6 (1956), 515-541 (in Chinese). Zbl0075.25003
  14. [14] K.-M. Tsang, Higher power moments of Δ(x), E(t) and P(x), Proc. London Math. Soc. (3) 65 (1992), 65-84. Zbl0725.11046

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