Some Ω -results related to the fourth power moment of the Riemann zeta-function and to the additive divisor problem

Jerzy Kaczorowski; Bogdan Szydło

Journal de théorie des nombres de Bordeaux (1997)

  • Volume: 9, Issue: 1, page 41-50
  • ISSN: 1246-7405

Abstract

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We improve the “two-sided” omega results in the fourth power mean problem for the Riemann zeta-function and in the additive divisor problem.

How to cite

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Kaczorowski, Jerzy, and Szydło, Bogdan. "Some $\Omega $-results related to the fourth power moment of the Riemann zeta-function and to the additive divisor problem." Journal de théorie des nombres de Bordeaux 9.1 (1997): 41-50. <http://eudml.org/doc/247990>.

@article{Kaczorowski1997,
abstract = {We improve the “two-sided” omega results in the fourth power mean problem for the Riemann zeta-function and in the additive divisor problem.},
author = {Kaczorowski, Jerzy, Szydło, Bogdan},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Riemann zeta-function; fourth power moment; -results; spectral theory; asymptotic formula; additive divisor problem},
language = {eng},
number = {1},
pages = {41-50},
publisher = {Université Bordeaux I},
title = {Some $\Omega $-results related to the fourth power moment of the Riemann zeta-function and to the additive divisor problem},
url = {http://eudml.org/doc/247990},
volume = {9},
year = {1997},
}

TY - JOUR
AU - Kaczorowski, Jerzy
AU - Szydło, Bogdan
TI - Some $\Omega $-results related to the fourth power moment of the Riemann zeta-function and to the additive divisor problem
JO - Journal de théorie des nombres de Bordeaux
PY - 1997
PB - Université Bordeaux I
VL - 9
IS - 1
SP - 41
EP - 50
AB - We improve the “two-sided” omega results in the fourth power mean problem for the Riemann zeta-function and in the additive divisor problem.
LA - eng
KW - Riemann zeta-function; fourth power moment; -results; spectral theory; asymptotic formula; additive divisor problem
UR - http://eudml.org/doc/247990
ER -

References

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  2. [2] J.-M. Deshouillers, H. Iwaniec, Additive divisor problem, J. London Math. Soc., 26(2), (1982), 1-14. Zbl0462.10030MR667238
  3. [3] A. Ivić, Y. Motohashi, On the fourth power moment of the Riemann zeta-function, J. Number Theory51(1995), 16-45. Zbl0824.11048MR1321722
  4. [4] A. Ivić, Y. Motohashi, The mean square of the error term for the fourth moment of the zeta-function, Proc. London Math. Soc. (3)69(1994), 309-329. Zbl0805.11060MR1281967
  5. [5] M. Jutila, The additive divisor problem and exponential sums, Proc. Third Conf. Canadian Number Theory Association (Kingston1991), Clarendon Press, Oxford1993, 113-135. Zbl0792.11037MR1368414
  6. [6] J. Kaczorowski, Results on the distribution of primes, J. reine angew. Math., 446(1994), 89-113. Zbl0783.11033MR1256149
  7. [7] E. Landau, Ueber einen Satz von Tschebyschef, Math. Ann.61(1905), 527-550. MR1511360JFM37.0224.04
  8. [8] Y. Motohashi, Spectral mean values of Maass waveform L-functions, J. Number Th.42(1992), 258-284. Zbl0759.11026MR1189505
  9. [9] Y. Motohashi, The binary additive divisor problem, Ann Sci. L'Ecole Norm. Sup., 27(4)(1994), 529-572. Zbl0819.11038MR1296556
  10. [10] Y. Motohashi, A relation between the Riemann zeta-function and the hyperbolic Laplacian, Ann. Sc. Norm. Sup. Pisa Cl. Sci., 22(4)(1995), 299-313. Zbl0831.11046MR1354909
  11. [11] B. Szydlo, On oscillations in the additive divisor problem, I, Acta Arith., 66(1994), 63-69. Zbl0805.11068MR1262653
  12. [12] L.A. Tahtadjan, A.I. Vinogradov, The zeta-function of the additive divisor problem and the spectral decomposition of the automorphic Laplacian, Zap. Nauch. Sem. LOMI, ANSSSR134, (1984), 84-116, (Russian). Zbl0536.10025MR741855

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