Exponential sums modulo prime powers

Acta Arithmetica

Volumn 101, Issue 2, 2002, Pages 131-149

  Cochrane, Todd ^a  

^a KANSAS STATE UNIVERSITY   (United States)

Author keywords

Exponential sums

Indexed keywords

EID: 0041469804     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa101-2-5     Document Type: Article

References (32)

1. E. Bombieri, On exponential sums in finite fields, Amer. J. Math. 88 (1966), 71-105.
2. J. H. H. Chalk, On Hua's estimate for exponential sums, Mathematika 34 (1987), 115-123.
3. T. Cochrane and Z. Y. Zheng, Pure and mixed exponential sums, Acta Arith. 91 (1999), 249-278.
4. _, _, Exponential sums with rational function entries, ibid. 95 (2000), 67-95.
5. _, _, On upper bounds of Chalk and Hua for exponential sums, Proc. Amer. Math. Soc. 129 (2001), 2505-2516.
6. mℤ and applications to GL(3)-Kloosterman sums, Acta Arith. 80 (1997), 1-48.
7. P. Ding, An improvement to Chalk's estimation of exponential sums, ibid. 59 (1991), 149-155.
8. _, On a conjecture of Chalk, J. Number Theory 65 (1997), 116-129.
9. D. Ismoilov, Estimate of a character sum of polynomials, Dokl. Akad. Nauk Tadzhik. SSR 29 (1986), 567-571 (in Russian).
10. _, Estimate of a character sum of rational functions, ibid., 635-639 (in Russian).
11. _, Estimates for character sums of polynomials and rational functions, in: Construction Methods and Algorithms in Number Theory, Abstracts of Reports, Minsk, 1989, 62 (in Russian).
12. _, On lower bounds of character sums of rational functions with respect to a composite modulus, Vestnik Tadzhik. Cos. Univ. Mat. 5 (1990), 27-32 (in Russian).
13. _, Lower bounds on character sums of polynomials with respect to a composite modulus, Dokl. Akad. Nauk Tadzhik. SSR 33 (1990), 501-505 (in Russian).
14. _, Estimates of complete character sums of polynomials, Trudy Mat. Inst. Steklov. 200 (1991), 171-186 (in Russian); English transl.: Proc. Steklov Inst. Math. 200 (1993), 189-203.
15. _, Estimates of complete character sums of polynomials, Trudy Mat. Inst. Steklov. 200 (1991), 171-186 (in Russian); English transl.: Proc. Steklov Inst. Math. 200 (1993), 189-203.
16. _, A lower bound estimate for complete sums of characters of polynomials and rational functions, Acta Math. Sinica (N.S.) 9 (1993), 90-99.
17. _, Estimates for complete trigonometric sums, Number Theory and Analysis, Trudy Mat. Inst. Steklov. 207 (1994), 153-171 (in Russian); English transl.: Proc. Steklov Inst. Math. 207 (1995), 137-153.
18. _, Estimates for complete trigonometric sums, Number Theory and Analysis, Trudy Mat. Inst. Steklov. 207 (1994), 153-171 (in Russian); English transl.: Proc. Steklov Inst. Math. 207 (1995), 137-153.
19. N. Katz, Gauss Sums, Kloosterman Sums and Monodromy Groups, Ann. of Math. Stud. 116, Princeton Univ. Press, Princeton, 1988.
20. C. L. Liu, Character sums of rational functions, Sci. China Ser. A 38 (1995), 182-187.
21. _, Dirichlet character sums, Acta Arith. 88 (1999), 299-309.
22. _, Dirichlet character sums of rational functions, preprint, 2000.
23. W. K. A. Loh, Hua's Lemma, Bull. Austral. Math. Soc. 50 (1994), 451-458.
24. J. H. Loxton and R. C. Vaughan, The estimation of complete exponential sums, Canad. Math. Bull. 28 (1985), 442-454.
25. α I, Proc. Japan Acad. Ser. A 59 (1983), 109-112.
26. α II, ibid., 161-163.
27. n), n ≥ 2, Bull. London Math. Soc. 5 (1973), 325-327.
28. G. I. Perelmuter, Estimate of a sum along an algebraic curve, Mat. Zametki 5 (1969), 373-380 (in Russian).
29. A. G. Postnikov, On a character sum modulo a prime power of a prime, Izv. Akad. Nauk SSSR Ser. Mat. 19 (1955), 11-16 (in Russian).
30. H. Salié, Über die Kloostermanschen Summen S(u,v;q), Math. Z. 34 (1931), 91-109.
31. W. M. Schmidt, Equations over Finite Fields, Lecture Notes in Math. 536, Springer, Berlin, 1976.
32. S. A. Stepanov, Arithmetic of Algebraic Curves, Monographs in Contemporary Mathematics, Consultants Bureau, New York, 1994.