85. M. Z. Garaev, J. C. Hernandez, A note on n! modulo p, Monatschefte fur Mathematik, (to appear).

84. J. CIlleruelo, M. Z. Garaev, The congruence x x = λ (mod p), Proc. Amer. Math. Soc. (to appear).

83. J. CIlleruelo, M. Z. Garaev, Congruences involving product of intervals and sets with small multiplicative doubling modulo a prime and applications, Math. Proc. Cambridge Phil. Soc. (to appear)

82. J. Bourgain, M. Z. Garaev, S. V. Konyagin, I. E. Shparlinski, Multiplicative congruences with variables from short intervals, Journal d'Analyse Mathematique, 124 (2014), 117--147.

81. M.-C. Chang, J. Cilleruelo, M. Z. Garaev, J. Hernandez, I. E. Shparlinski, A. Zumalacarregui, Points on curves in small boxes and applications, Mich. Math. J. 63 (2014), 503–534.

80. J. Bourgain, M. Z. Garaev, Sumsets of reciprocals in prime fields and multilinear Kloosterman sums, Izvestiya RAN., Ser. Mat., 78(4) (2014), 19–72.

79. J. Bourgain, M. Z. Garaev, Kloosterman sums in residue rings, Acta Arithmetica, 164 (2014), 43-64.

78. M. Z. Garaev, S. V. Konyagin, Multiplicative decomposition of arithmetic progressions in prime fileds, J. Number Theory, 145 (2014), 540--553.

77. M. Z. Garaev, Sum-product theorems and applications, pp. 185-192 of the Handbook of Finite Fields by Gary L. Mullen and Daniel Panario. Published June 17, 2013 by Chapman and Hall/CRC.

76. J. Bourgain, M. Z. Garaev, S. V. Konyagin, I. E. Shparlinski, On congruences with products of variables from short intervals and applications. Proc. Steklov Inst. Math. 280 (2013), 67-96. Special issue dedicated to 60-th anniversary of Akademik B. S. Kashin.

75. J. Bourgain, M. Z. Garaev, S. V. Konyagin, I. E. Shparlinski, On the hidden shifted power problem, SIAM J. Comp. 41(6) (2012), 1524-1557.

74. J. Cilleruelo, M. Z. Garaev, A. Ostafe, I.E. Shparlinski, On the concentration of points of polynomial maps and applications, Math. Zeitschrift. 272(3-4) (2012), 825-837.

73. M. Z. Garaev, On multiplicative congruences, Math. Zeitschrift. 272(1-2) (2012), 473-482

72. W. D. Banks, J. Friedlander, M. Z. Garaev, I. E. Shparlinski, Exponential and character sums with Mersenne Numbers, J. Aust. Math. Soc. 92 (2012), 1-13. In memory of Professor Alf van der Poorten.

71. M. Z. Garaev, S. V. Konyagin, Yu. V. Malykhin, The asymptotic for the sum of powers of distances between power residues modulo a prime, Proc. Steklov Inst. Math. 276 (2012), 83-95.

70. J. Cilleruelo, M. Z. Garaev, Concentration of points on two and three dimensional modular hyperbolas and applications, Geometric and Functional Analysis, 21 (2011), 892-904.

69. M. Z. Garaev, On the number of common values of arithmetic functions φ and σ below x, Moscow J. Combinatorics and Number Theory, Vol 1, no. 3 (2011), 42-49.

68. M. Z. Garaev, An estimate of Kloosterman sums with prime numbers and application, Math. Notes 88:3 (2010), 330-337. In memory of Professor A. A. Karatsuba.

67. M. Z. Garaev, Sums and products of sets and rational trigonometric sum estimates in prime fields, Russian Math. Surveys 394 no. 65:4 (2010), 5-66.

66. M. Z. Garaev, C.-Y. Shen, On the size of the set A(A+1), Math. Zeitschrift 265 (2010), 125-132.

65. J. Cilleruelo, M. Z. Garaev, Least totients in arithmetic progressions, Proc. Amer. Math. Soc. 137 (2009), 2913-2919.

64. M. Z. Garaev, A note on the least totient of a residue class, Quart. J. Math. 60 (2009), 53-56.

63. M.Z. Garaev, Sumas trigonometricas y congruencias aditivas, La Gaceta de la RSME 12 (2009), 129-143.

62. J. Bourgain, M. Z. Garaev,On a variant of sum-product estimates and explicit exponential sum bounds in prime fields, Math. Proc. Cambridge Phil. Soc. 146 (1) (2009), 1-21.

61. M. Z. Garaev, V. C. Garcia, S. V. Konyagin, Waring problem with the Ramanujan τ-function, II, Canadian Math. Bull. 52 (2009), 195-199.

60. M. Z. Garaev, The large sieve inequality for the exponential sequence λ^{[O(n^{15/14+o(1)})]} modulo primes, Canadian J. Math. 61 (2009), 336-350.

59. W. D. Banks, M. Z. Garaev, F. Luca, I. E. Shparlinski, Uniform distribution of fractional parts related to pseudoprimes, Canadian J. Math. 61 (2009), pp. 481-502.

58. M. Z. Garaev, The sum product estimate for large subsets of prime fields, Proc. Amer. Math. Soc. 136 (2008), 2735-2739.

57. M. Z. Garaev, A quantified version of Bourgain's sum-product estimate in F_p for subsets of incomparable sizes, Electronic J. Combinatorics 15 (2008), #R58.

56. M. Z. Garaev, V. C. Garcia, The equation x1x2=x3x4+λ in fields of prime order and applications, J. Number Theory 128 (2008), 2520-2537.

55. W. D. Banks, M. Z. Garaev, D. R. Heath-Brown, I. E. Shparlinski, Density of non-residues in Burgess-type intervals and applications, Bull. London Math. Soc. 40 (2008), 88-96.

54. M. Z. Garaev, V. C. Garcia, S. V. Konyagin, Waring problem with the Ramanujan τ-function, Izv. Math. RAS 71 (2008), 39-50.

53. M. Z. Garaev, M. Kuhleitner, F. Luca, W. G. Nowak, Asymptotic formulas for certain arithmetics functions, Math. Slovaca 58 (2008), 301-308.

52. M. Z. Garaev, C. Y. Yildirim, On small distances between ordinates of zeros of ζ(s) and ζ'(s), Int. Math. Res. Notices no.21 (2007), Art.Id.rnm091.

51. M. Z. Garaev, An explicit sum-product estimate in F_p, Int. Math. Res. Notices no.11 (2007), Art. Id.rnm035.

50. M. Z. Garaev, V. C. Garcia, S. V. Konyagin, A note on the Ramanujan τ-function, Archiv der Math. 89 (2007), 411-418.

49. M. Z. Garaev, On the number of solutions of a diophantine equation with symmetric entries, J. Number Theory 125 (2007), 201-209.

48. M. Z. Garaev, V. C. Garcia, Waring type congruences involving factorials modulo a prime, Archiv der Math. 88 (2007), 35--41.

47. M. Z. Garaev, A. A. Karatsuba, The representation of residue classes by products of small integers, Proc. Edinburgh Math. Soc. 50 (2007), 363--375.

46. M. Z. Garaev, On an additive representation associated with the L_1-norm of an exponential sum, Rocky Mountain J. Math. 37 (5) (2007), 1551-1556.

45. M. Z. Garaev, F. Luca, I. E. Shparlinski,Exponential sums with Catalan numbers and middle binomial coefficients, Indag. Math (N. S.) 18 (1) (2007), 23--37.

44. E. Balanzario, M. Z. Garaev, R. Zuazua-Vega, Exceptional set of a representation with fractional powers, Acta Math. Hungarica 114 (2007), 103-115.

43. M. Z. Garaev, On the logarithmic factor in error term estimates in certain additive congruence problems, Acta Arith. 124 (2006), 27-39.

42. M. Z. Garaev, A. A. Karatsuba, New estimates of double trigonometric sums with exponential functions, Archiv der Math. 87 (2006), 33-40.

41. W. D. Banks, J. B. Friedlander, M. Z. Garaev, I. E. Shparlinski, Character sums with exponential functions over smooth numbers, Indag. Math. (N.S.) 17 (2006), 157-168.

40. M. Z. Garaev, F. Luca, W. G. Nowak, Short interval asymptotics for a class of arithmetical function, Acta Math. Hungarica 113 (2006), 85-99.

39. M. Z. Garaev, F. Luca, I. Shparlinski, A. Winterhof, On the linear complexity over F_p of Sidelnikov sequences, IEEE Trans. Inform. Theory 52 (2006), 3299-3304.

38. M. Z. Garaev, Character sums in short intervals and the multiplication table modulo a large prime, Monatshefte fur Math. 148 (2006), 127-138.

37. M. Z. Garaev, F. Luca, I. E. Shparlinski, Distribution of harmonic sums and Bernoulli polynomials modulo a prime, Math. Zeitschrift 253 (2006), 855-865.

36. M. Z. Garaev, F. Luca, I. E. Shparlinski, Catalan and Apery numbers in residue classes, J. Combin. Theory Ser. A 113 (2006), 851-865.

35. M. Z. Garaev, A. A. Sankaranarayanan, The sum involving derivative of ζ(s) over simple zeros, J. Number Theory, 117 (2006), 122-130.

34. W. D. Banks, J. B. Friedlander, M. Z. Garaev, I. E. Shparlinski, Double character sums over finite fields and elliptic curves and their applications, Pure Appl. Math. Quart., Vol. 2, No.1 (2006), 179-197. Special Issue in honor of John H. Coates,

33. M. Z. Garaev, F. Luca, W. G. Nowak, The divisor problem for d_4(n) in short intervals, Archiv der Math. 86 (2006), 60-66.

32. M. Z. Garaev, Double exponential sums related to Diffie-Hellman distribution, Int. Math. Res. Notices 17 (2005), 1005-1014.

31. M. Z. Garaev, Upper bounds for the number of solutions of a diophantine equation, Trans. Amer. Math. Soc. 357:6 (2005), 2527-2534.

30. M. Z. Garaev, F. Luca, I. E. Shparlinski, Exponential sums and congruences with factorials, J. Reine Angew. Math. 584 (2005), 29-44.

29. M. Z. Garaev, I. E. Shparlinski, The large sieve inequality with exponential functions and the distribution of Mersenne numbers modulo primes,Int. Math. Res. Notices 39 (2005), 2391-2408.

28. W. D. Banks, M. Z. Garaev, F. Luca, I. E. Shparlinski, Uniform distribution of the fractional part of the average prime divisor, Forum Math. 17 (2005), 885-901.
27. M. Z. Garaev, A. A. Karatsuba, On character sums and the exceptional set of a congruence problem, J. Number Theory 114 (2005), 182-192.

26. M. Z. Garaev, F. Luca, Character sums and product of factorials modulo p, J. Theor. des Nombres de Bordeaux 17:1 (2005), 151-160.

25. M. Z. Garaev, F. Luca, I. E. Shparlinski, Waring problem with factorials, Bull. Austral. Math. Soc. 71 (2005), 259-264.

24. M. Z. Garaev, K. L. Kueh, On cardinality of sumsets, J. Austral. Math. Soc. 78 (2005), 221-226.

23. M. Z. Garaev, F. Luca, I. E. Shparlinski, Character sums and congruences with n!, Trans. Amer. Math. Soc. 356:12 (2004) 5089-5102.

22. M. Z. Garaev, One inequality involving simple zeros of ζ(s), Hardy-Ramanujan Journal 26 (2004), 18-22.

21. M. Z. Garaev, On vertical zeros of Re ζ(s) and Im ζ(s), Acta Arith. 108.3 (2003), 245-251.

20. M. Z. Garaev, On the Waring-Goldbach problem with small non-integer exponent, Acta Arith. 108.3 (2003), 297-302.

19. M. Z. Garaev, A note on the least quadratic non-residue of the integer-sequences, Bull. Austral. Math. Soc. 68 (2003), 1-11.

18. M. Z. Garaev, On a series with simple zeros of ζ(s), Math. Notes 73:4 (2003), 58-587.

17. M. Z. Garaev, K. L. Kueh, Distribution of special sequences modulo a large prime, Int. J. of Math. and Math. Sci. 50 (2003), 3189-3194.

16. M. Z. Garaev, Concerning the Karatsuba conjectures, Taiwanese J. Math. 6 (2002), 573-580.

15. M. Z. Garaev, On a multiple trigonometric series, Acta Arith. 102.2 (2002), 183-187.


14. M. Z. Garaev, K. L. Kueh, On the equation x^2-Ny^n=-1, Chebyshev's Sbornik, 3 (2002), 136-140. Dedicated to the anniversary of Professor N. M. Korobov.

13. M. Z. Garaev, K. L. Kueh, L_1- norms of exponential sums and the corresponding additive problem, Z. Anal. Anwendungen 20:4 (2001), 999-1006.

12. M. Z. Garaev, On the diophantine equation (x+y+z)^3 = nxyz, Moscow Univ. Math. Bull. 1 (2001), p. 46.

11. M. Z. Garaev, On the Diophantine equation (x/y)^u+(y/z)^v+(z/x)^w=4t, (in Russian), Fundam. Prikl. Mat. 7:1 (2001), 267-270.

10. M. Z. Garaev, Some relations between arguments of Gauss sums, Doklady Math. 62:3 (2000), 339-340.

9. M. Z. Garaev, On lower bounds for the L_1- norm of exponential sums, Math. Notes 68:6 (2000), 713--720.

8. M. Z. Garaev, On arguments of Gauss sums, Moscow Univ. Math. Bull. 6 (2000), 52-55.

7. M. Z. Garaev, On the Gauss trigonometric sums, Math. Notes 68:2 (2000), 154-158.

6. M. Z. Garaev, V. N. Chubarikov, Concerning the Sierpinski-Schinzel system of diophantine equations, Math. Notes 66:2 (1999), 181-187.

5. M. Z. Garaev, Kh. Kh. Pilehrud, A remark on a system of Diophantine Pell equations, (in Russian), Fundam. Prikl. Mat. 5:3 (1999), 927-930.

4. M. Z. Garaev, On oscillating third-order differential equations, Moscow Univ. Math. Bull. 4 (1999), 50-51.

3. M. Z. Garaev, Third-degree diophantine equations, Proc. Steklov Inst. Math. 218 (1997), 94-103.

2. M. Z. Garaev, On the Diophantine equation x^3+y^3+z^3=nxyz, (in Russian), Moscow Univ. Math. Bull. 2 (1997), 40-41.

1. M. Z. Garaev, On the asymptotic behavior of solutions of higher-order linear differential equations, (in Russian), Fundam. Prikl. Mat. 1:3 (1995), 801-804.