Research Papers  (dvi files)

  1. Bounds on exponential sums and the polynomial Waring's problem mod p, with C. Pinner and J. Rosenhouse, to appear in Proc. London Math. Soc..               
  2. Upper bounds on character sums with rational function entries, with Chun-Lei Liu and Zhiyong Zheng, to appear in Acta Mathematica Sinica.                           
  3. U pper bounds on a two-term exponential sum ,  with Z. Zheng,   Science in China (Series A) 44, No. 8, (2001), 1003-1015.

    4.  
  4. Bounds for certain exponential sums,   with Z. Zheng,  Asian Journal of Mathematics 4, no. 4, (2002), 757-774.

    5.  
  5. Exponential sums modulo prime powers ,   Acta Arithmetica 101, no. 2, (2002), 131-149.

    6.  
  6. On upper bounds of Chalk and Hua for exponential sums,    with Z. Zheng, Proc. Amer. Math. Soc. 129, no. 9, (2001), 2505-2516.

    7.  
  7. A survey on pure and mixed exponential sums modulo prime powers ,    with Z. Zheng, Proc. Illinois Millennial conf. on Number Theory (2002).

    8.  
  8. Exponential sums with rational function entries,   with  Z. Zheng, Acta Arithmetica 95, no. 1  (2000), 67-95.

    9.  
  9.   Upper bounds on n-dimensional Kloosterman sums , with M.C. Liu and Z. Zheng, Preprint (2000).

    10.  
  10.  P ure and Mixed exponentia l sums,   with Z. Zheng ,  Acta Arithmetica 91, no. 3, (1999), 249-278.

    11.  
  11. A n asymptotic formula for a trigonometric sum of Vinogradov,   with J.C. Peral,  J. Number Theory 91 (2001), 1-19.

    12.  
  12.  On a problem of H. Cohn for character sums ,  with D. Garth and Z. Zhiyong,  J. Number Theory 81 (2000), 120-129.

    13.  
  13. Gaps between integers with the same prime factors, with R. Dressler, Math. Comp. 68 no. 225 (1999), 395-401.

    14.  
  14. S mall solutions of the Legendre equation,  with P. Mitchell, J. Number Theory 70 no. 1 (1998), 62-66.

    15.  
  15. H igh order moments of character sums, with Z. Zheng, Proc. Amer. Math. Soc. 126 no. 4 (1998), 951-956.

    16.  
  16. T he congruence x_1x_2=x_3x_4 (mod p) , the equation x_1x_2=x_3x_4 and mean values of character sums, with A. Ayyad and Z. Zheng, J. Number Theory 59 no. 2 (1996), 398-413.

    17.  
  17. B ounds on complete exponential sums, Analytic Number Theory: Proc. of the conference in honor of Heini Halberstam, Vol. 1, Birkhauser, Boston (1996), 211-224.

    18.  
  18. Covering congruences in higher dimensions, with G. Myerson, Rocky Mountain J. of Math. 26 no. 1 (1996), 77-81.

    19.  
  19. Small zeros of quadratic congruences modulo pq, II, J. Number Theory 50 no. 2 (1995), 299-308

    20.  
  20. Exponential sums and the distribution of solutions of congruences, Institute of Math., Academia Sinica, Taipei, Taiwan (1994).

    21.  
  21. O n representing the multiple of a number by a quadratic form, Acta Arith. 63 no. 3 (1993), 211-222.

    22.  
  22. Small zeros of quadratic forms modulo p, III, J. Number Theory 37 no. 1 (1991), 92-99.

    23.  
  23. Small zeros of quadratic congruences modulo pq, Mathematika 37 (1990), 261-272.

    24.  
  24. Small zeros of quadratic forms modulo p, II, Proc. Illinois Number Theory Conference of 1989, Birkhauser, Boston (1990), 91-94.

    25.  
  25. The diophantine equation f(x)=g(y), Proc. of the A.M.S. 109 no. 3 (1990), 573-577.

    26.  
  26. Small solutions of cubic congruences, Proc. of the A.M.S. 106 no. 2 (1989), 333-334.

    27.  
  27. Strong Riesz sets and polynomials, with R.E. Dressler, Colloquium Math. 58 (1989), 23-27.

    28.  
  28. Small zeros of quadratic forms modulo p, J. Number Theory 33 no. 3 (1989), 286-292.

    29.  
  29. Trigonometric approximation and uniform distribution modulo one, Proc. of the A.M.S. 103 no. 3 (1989), 695-702.
  30. Consecutive triples of sums of two squares, with R.E. Dressler, Archiv der Math. 49 (1987), 301-304.

    31.  
  31. On a trigonometric inequality of Vinogradov, J. Number Theory 26 no. 1 (1987), 9-16.

    32.  
  32. Small solutions of congruences over algebraic number fields,   Illinois J. of Math. 31 no. 4 (1987), 618-625.

    33.  
  33. An upper bound for character sums, preprint (1987).