Estimates for complete multiple exponential sums

J. H. Loxton

Acta Arithmetica (2000)

  • Volume: 92, Issue: 3, page 277-290
  • ISSN: 0065-1036

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J. H. Loxton. "Estimates for complete multiple exponential sums." Acta Arithmetica 92.3 (2000): 277-290. <http://eudml.org/doc/207388>.

@article{J2000,
author = {J. H. Loxton},
journal = {Acta Arithmetica},
keywords = {complete multiple exponential sums; Weil conjectures; Newton polyhedron},
language = {eng},
number = {3},
pages = {277-290},
title = {Estimates for complete multiple exponential sums},
url = {http://eudml.org/doc/207388},
volume = {92},
year = {2000},
}

TY - JOUR
AU - J. H. Loxton
TI - Estimates for complete multiple exponential sums
JO - Acta Arithmetica
PY - 2000
VL - 92
IS - 3
SP - 277
EP - 290
LA - eng
KW - complete multiple exponential sums; Weil conjectures; Newton polyhedron
UR - http://eudml.org/doc/207388
ER -

References

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  1. G. I. Arkhipov, A. A. Karatsuba and V. N. Chubarikov, Theory of Multiple Exponential Sums, Moscow, 1987 (in Russian). Zbl0638.10037
  2. K. A. Atan and J. H. Loxton, Newton polyhedra and solutions of congruences, in: Diophantine Analysis, J. H. Loxton and A. J. van der Poorten (eds.), London Math. Soc. Lecture Note Ser. 109, Cambridge, 1986, 67-82. Zbl0601.12023
  3. V. N. Chubarikov, Multiple rational trigonometric sums and multiple integrals, Mat. Zametki 20 (1976), 61-68 (in Russian); English transl.: Math. Notes 20 (1976). Zbl0353.10028
  4. P. Deligne, La conjecture de Weil. I, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 273-307. 
  5. G. H. Hardy and J. E. Littlewood, A new solution of Waring's problem, Quart. J. Math. 48 (1919), 272-293. Zbl47.0114.01
  6. S. W. Graham and G. Kolesnik, Van der Corput's Method of Exponential Sums, London Math. Soc. Lecture Note Ser. 126, Cambridge, 1991. Zbl0713.11001
  7. W. K. A. Loh, Exponential sums on reduced residue systems, Canad. Math. Bull. 41 (1997), 187-195. Zbl0944.11025
  8. J. H. Loxton and R. A. Smith, Estimates for multiple exponential sums, J. Austral. Math. Soc. 33 (1982), 125-134. Zbl0493.10041
  9. J. H. Loxton and R. C. Vaughan, The estimation of complete exponential sums, Canad. Math. Bull. 28 (1985), 440-454. Zbl0575.10033
  10. E. C. Titchmarsh, On Epstein's zeta function, Proc. London Math. Soc. (2) 36 (1934), 485-500. Zbl0008.30101
  11. R. C. Vaughan, The Hardy-Littlewood Method, Cambridge Tracts in Math. 80, Cambridge, 1981. 
  12. H. Weyl, Über die Gleichverteilung von Zahlen mod Eins, Math. Ann. 77 (1916), 313-352. Zbl46.0278.06

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