ArticleOriginal scientific text
Title
On sums of two kth powers: an asymptotic formula for the mean square of the error term
Authors 1
Affiliations
- Institut für Mathematik, Universität für Bodenkultur, A-1180 Wien, Austria
Bibliography
- A. S. Besicovitch, On the linear independence of fractional powers of integers, J. London Math. Soc. 15 (1940), 3-6.
- 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).
- K. S. Gangadharan, Two classical lattice point problems, Proc. Cambridge Philos. Soc. 57 (1961), 699-721.
- S. W. Graham and G. Kolesnik, Van der Corput's Method of Exponential Sums, Cambridge Univ. Press, Cambridge, 1991.
- J. L. Hafner, New omega theorems for two classical lattice point problems, Invent. Math. 63 (1981), 181-186.
- G. H. Hardy, On the expression of a number as the sum of two squares, Quart. J. Math. 46 (1915), 263-283.
- M. N. Huxley, Exponential sums and lattice points II, Proc. London Math. Soc. 66 (1993), 279-301.
- M. N. Huxley, Area, Lattice Points, and Exponential Sums, London Math. Soc. Monographs (N.S.) 13, Oxford, 1996.
- I. Kátai, The number of lattice points in a circle, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 8 (1965), 39-60.
- E. Krätzel, Lattice Points, Deutsch. Verlag Wiss., Berlin, 1988.
- E. Krätzel, Bemerkungen zu einem Gitterpunktproblem, Math. Ann. 179 (1969), 90-96.
- G. Kuba, On sums of two k-th powers of numbers in residue classes II, Abh. Math. Sem. Univ. Hamburg 63 (1993), 87-95.
- 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.
- W. G. Nowak, On sums of two k-th powers: a mean-square bound for the error term, Analysis 16 (1996), 297-304.
- W. G. Nowak, Sums of two k-th powers: an Omega estimate for the error term, Arch. Math. (Basel) 68 (1997), 27-35.
- D. Redmond, Mean value theorems for a class of Dirichlet series, Pacific J. Math. 78 (1978), 191-231.
- L. Schnabel, Über eine Verallgemeinerung des Kreisproblems, Wiss. Z. Friedrich-Schiller-Univ. Jena Math.-Natur. Reihe 31 (1982), 667-781.
- J. D. Vaaler, Some extremal problems in Fourier analysis, Bull. Amer. Math. Soc. 12 (1985), 183-216.
- J. G. van der Corput, Over roosterpunkten in het plate vlak, thesis, Groningen, 1919.