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Bounds for solutions of two additive equations of odd degree

Seria
Rozprawy Matematyczne tom/nr w serii: 271 wydano: 1989
Zawartość
Warianty tytułu
Abstrakty
EN

CONTENTS
1. Introduction...........................................................5
2. Initial reductions....................................................9
3. Local information.................................................10
4. Global reduction..................................................17
5. Preparation for the analytic argument.................28
6. Estimates for T(Λ)...............................................32
7. The minor arcs....................................................34
8. Estimates for treatment of the major arcs............36
9. Rational approximations in the major arcs...........40
10. Modifying the major arcs...................................43
11. The asymptotic formula.....................................47
References.............................................................52
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 271
Liczba stron
52
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCLXXI
Daty
wydano
1989
Twórcy
  • Deparment of Mathematics, University of Michigan, U.S.A
Bibliografia
  • Birch, B. J. (1957), Homogeneous forms of odd degree in a large number of variables, Mathematika 4, 102-105.
  • Cook, R. J. (1971a), Simultaneous solutions of additive Diophantine equations and inequalities, Ph. D. thesis, London.
  • Cook, R. J. (1971b), Simultaneous quadratic equations, J. London Math. Soc. (2) 4, 319-326.
  • Cook, R. J. (1972a), A note on a lemma of Hua, Quart. J. Math. (Oxford) (2) 23, 287-288.
  • Cook, R. J. (1972b), Pairs of additive equations, Michigan Math. J. 19, 325-331.
  • Davenport, H. (1939a), On Waring's Problem for cubes, Acta Math. 71, 123-143.
  • Davenport, H. (1939b), On Waring's Problem for fourth powers, Ann. Math. 40, 731-747.
  • Davenport, H. (1962), Analytic methods for Diophantine_equations and inequalities, Campus Publishers, Ann Arbor.
  • Davenport, H. (1977), The Collected Works of 'Harold Davenport, Vol. Ill ed. B. J. Birch, H. Halberstam and C. A. Rogers, Academic Press, London.
  • Davenport, H. and Heilbornn, H. (1936), On an exponential sum, Proc. London Math. Soc. (2) 41, 449-453.
  • Davenport, H. and Heilbronn, H. (1937), On Waring's Problem: Two cubes and one square, Proc. London Math. Soc. (2) 43, 73-104.
  • Davenport, H. and Lewis, D. J. (1963), Homogeneous additive equations, Proc. Roy. Soc. A274, 443 -460.
  • Davenport, H. and Lewis, D. J. (1966), Cubic equations of additive type, Phil. Trans. Roy. Soc. A 261, 97-136.
  • Davenport, H. and Lewis, D. J. (1969a), Simultaneous equations of additive type, Phil. Trans. Roy. Soc. A264, 557-595.
  • Davenport, H. and Lewis, D. J. (1969b), Two additive equations, Amer. Math. Soc. Proc., Symposia in Pure Mathematics 12, 74-98.
  • Lewis, D. J. (1957), Cubic congruences, Michigan Math. J. 4, 85-95
  • Lewis, D. J. (1970), Systems of Diophantine equations, Instituto Nazionale di Alta Matematica, Symposia Mathematica 4, 33-43.
  • Lloyd, D. P. (1975), Bounds for solutions of Diophantine equations, Ph. D. thesis, University of Adelaide.
  • Pitman, Jane (1971), Bounds for solutions of diagonal equations. Acta Arith. 19, 223-247.
  • Pitman, Jane (1981), Pairs of diagonal inequalities, Recent Progress in analytic number theory, Vol. 2 (Durham, 1979), pp. 183-215, Academic Press, London.
  • Pitman, Jane and Ridout, D. (1967), Diophantine cubic equations and inequalities, Proc. Roy. Soc. A 297, 476-502..
  • Ponnudurai, T. (1979), Diophantine inequalities in many variables, Ph. D. thesis, University of Adelaide.
  • Schmidt, W. M. (1980), Diophantine inequalities for forms of odd degree, Adv. in Math. 33, no 2, 128-151.
  • Toliver, R. H. (1975), Bounds for solutions of two simultaneous additive equations of odd degree, Ph. D. thesis, The University of Michigan.
  • Toliver, R. H. (1977), A note on two additive cubic equations, unpublished manuscript.
  • Vaughan, R. C. (1977), On pairs of additive cubic equations, Proc, London Math. Soc. Ser. (3) 34, 354-364.
  • Vaughan, R. C. (1981), The Hardy-Littlewood Method, Cambridge University Press.
Języki publikacji
EN
Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-e679464d-8af9-409e-8440-2886b44f70f0
Identyfikatory
ISBN
83-01-08508-8
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki

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