On sums of two kth powers: an asymptotic formula for the mean square of the error term

M. Kühleitner

Acta Arithmetica (2000)

  • Volume: 92, Issue: 3, page 263-276
  • ISSN: 0065-1036

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M. Kühleitner. "On sums of two kth powers: an asymptotic formula for the mean square of the error term." Acta Arithmetica 92.3 (2000): 263-276. <http://eudml.org/doc/207387>.

@article{M2000,
author = {M. Kühleitner},
journal = {Acta Arithmetica},
keywords = {sums of two higher powers; asymptotic formula; mean square; functional equation},
language = {eng},
number = {3},
pages = {263-276},
title = {On sums of two kth powers: an asymptotic formula for the mean square of the error term},
url = {http://eudml.org/doc/207387},
volume = {92},
year = {2000},
}

TY - JOUR
AU - M. Kühleitner
TI - On sums of two kth powers: an asymptotic formula for the mean square of the error term
JO - Acta Arithmetica
PY - 2000
VL - 92
IS - 3
SP - 263
EP - 276
LA - eng
KW - sums of two higher powers; asymptotic formula; mean square; functional equation
UR - http://eudml.org/doc/207387
ER -

References

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  1. [1] A. S. Besicovitch, On the linear independence of fractional powers of integers, J. London Math. Soc. 15 (1940), 3-6. Zbl0026.20301
  2. [2] K. Corrádi and I. Kátai, A note on K. S. Gangadharan's paper 'Two classical lattice point problems' Magyar Tud. Akad. Mat. Fiz. Tud. Oszt. Kötzl. 17 (1967), 89-97 (in Hungarian). 
  3. [3] K. S. Gangadharan, Two classical lattice point problems, Proc. Cambridge Philos. Soc. 57 (1961), 699-721. Zbl0100.03901
  4. [4] S. W. Graham and G. Kolesnik, Van der Corput's Method of Exponential Sums, Cambridge Univ. Press, Cambridge, 1991. Zbl0713.11001
  5. [5] J. L. Hafner, New omega theorems for two classical lattice point problems, Invent. Math. 63 (1981), 181-186. Zbl0458.10031
  6. [6] G. H. Hardy, On the expression of a number as the sum of two squares, Quart. J. Math. 46 (1915), 263-283. Zbl45.1253.01
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  8. [8] M. N. Huxley, Area, Lattice Points, and Exponential Sums, London Math. Soc. Monographs (N.S.) 13, Oxford, 1996. 
  9. [9] I. Kátai, The number of lattice points in a circle, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 8 (1965), 39-60. Zbl0151.04401
  10. [10] E. Krätzel, Lattice Points, Deutsch. Verlag Wiss., Berlin, 1988. 
  11. [11] E. Krätzel, Bemerkungen zu einem Gitterpunktproblem, Math. Ann. 179 (1969), 90-96. 
  12. [12] G. Kuba, On sums of two k-th powers of numbers in residue classes II, Abh. Math. Sem. Univ. Hamburg 63 (1993), 87-95. Zbl0799.11037
  13. [13] M. Kühleitner, W. G. Nowak, J. Schoissengeier and T. Wooley, On sums of two cubes: an Ω₊-estimate for the error term, Acta Arith. 85 (1998), 179-195. Zbl0916.11052
  14. [14] W. G. Nowak, On sums of two k-th powers: a mean-square bound for the error term, Analysis 16 (1996), 297-304. Zbl0860.11060
  15. [15] W. G. Nowak, Sums of two k-th powers: an Omega estimate for the error term, Arch. Math. (Basel) 68 (1997), 27-35. Zbl0880.11066
  16. [16] D. Redmond, Mean value theorems for a class of Dirichlet series, Pacific J. Math. 78 (1978), 191-231. Zbl0364.10019
  17. [17] L. Schnabel, Über eine Verallgemeinerung des Kreisproblems, Wiss. Z. Friedrich-Schiller-Univ. Jena Math.-Natur. Reihe 31 (1982), 667-781. Zbl0497.10038
  18. [18] J. D. Vaaler, Some extremal problems in Fourier analysis, Bull. Amer. Math. Soc. 12 (1985), 183-216. Zbl0575.42003
  19. [19] J. G. van der Corput, Over roosterpunkten in het plate vlak, thesis, Groningen, 1919. 

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