On sums of two kth powers: an asymptotic formula for the mean square of the error term
M. Kühleitner
Acta Arithmetica, Tome 92 (2000), p. 263-276 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)
Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:207387 
@article{bwmeta1.element.bwnjournal-article-aav92i3p263bwm,
     author = {M. K\"uhleitner},
     title = {On sums of two kth powers: an asymptotic formula for the mean square of the error term},
     journal = {Acta Arithmetica},
     volume = {92},
     year = {2000},
     pages = {263-276},
     zbl = {0948.11035},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav92i3p263bwm}
}

M. Kühleitner. On sums of two kth powers: an asymptotic formula for the mean square of the error term. Acta Arithmetica, Tome 92 (2000) pp. 263-276. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav92i3p263bwm/

[000] [1] A. S. Besicovitch, On the linear independence of fractional powers of integers, J. London Math. Soc. 15 (1940), 3-6. | Zbl 0026.20301

[001] [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).

[002] [3] K. S. Gangadharan, Two classical lattice point problems, Proc. Cambridge Philos. Soc. 57 (1961), 699-721. | Zbl 0100.03901

[003] [4] S. W. Graham and G. Kolesnik, Van der Corput's Method of Exponential Sums, Cambridge Univ. Press, Cambridge, 1991. | Zbl 0713.11001

[004] [5] J. L. Hafner, New omega theorems for two classical lattice point problems, Invent. Math. 63 (1981), 181-186. | Zbl 0458.10031

[005] [6] G. H. Hardy, On the expression of a number as the sum of two squares, Quart. J. Math. 46 (1915), 263-283. | Zbl 45.1253.01

[006] [7] M. N. Huxley, Exponential sums and lattice points II, Proc. London Math. Soc. 66 (1993), 279-301. | Zbl 0820.11060

[007] [8] M. N. Huxley, Area, Lattice Points, and Exponential Sums, London Math. Soc. Monographs (N.S.) 13, Oxford, 1996.

[008] [9] I. Kátai, The number of lattice points in a circle, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 8 (1965), 39-60. | Zbl 0151.04401

[009] [10] E. Krätzel, Lattice Points, Deutsch. Verlag Wiss., Berlin, 1988.

[010] [11] E. Krätzel, Bemerkungen zu einem Gitterpunktproblem, Math. Ann. 179 (1969), 90-96.

[011] [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. | Zbl 0799.11037

[012] [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. | Zbl 0916.11052

[013] [14] W. G. Nowak, On sums of two k-th powers: a mean-square bound for the error term, Analysis 16 (1996), 297-304. | Zbl 0860.11060

[014] [15] W. G. Nowak, Sums of two k-th powers: an Omega estimate for the error term, Arch. Math. (Basel) 68 (1997), 27-35. | Zbl 0880.11066

[015] [16] D. Redmond, Mean value theorems for a class of Dirichlet series, Pacific J. Math. 78 (1978), 191-231. | Zbl 0364.10019

[016] [17] L. Schnabel, Über eine Verallgemeinerung des Kreisproblems, Wiss. Z. Friedrich-Schiller-Univ. Jena Math.-Natur. Reihe 31 (1982), 667-781. | Zbl 0497.10038

[017] [18] J. D. Vaaler, Some extremal problems in Fourier analysis, Bull. Amer. Math. Soc. 12 (1985), 183-216. | Zbl 0575.42003

[018] [19] J. G. van der Corput, Over roosterpunkten in het plate vlak, thesis, Groningen, 1919.