Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON THE r-TH HYPER-KLOOSTERMAN SUMS AND ITS HYBRID MEAN VALUE

  • Published : 2006.11.01
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Abstract

The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the T-th hyper-Kloosterman sums Kl(h, k+1, r;q) and the hyper Cochrane sums C(h, q; m, k), and give an interesting mean value formula.

Keywords

References

  1. D. Bump, W. Duke, J. Hoffstein, and H. Iwaniec, An estimate for the Hecke eigenvalues of Maass forms, Internat.Math. Res. Notices (1992), no. 4, 75-81
  2. W. Luo, Z. Rudnick, and P. Sarnak, On Selberg's eigenvalue conjecture, Geom. Funct. Anal. 5 (1995), no. 2, 387-401 https://doi.org/10.1007/BF01895672
  3. L. J. Mordell, On a special polynomial congruence and exponential sums : in 'Calcutta Math. Soc. Golden Jubilee Commemoration Volume' Part 1, Calcutta Math. Soc., Calcutta, 1963, pp. 29-32
  4. Chengdong Pan and Chengbiao Pan, Goldbach's Conjecture, Science Press, Bei- jing, 1981
  5. R. A. Smith, On n-dimensional Kloosterman sums, J. Number Theory 11 (1979), no. 3, 324-343 https://doi.org/10.1016/0022-314X(79)90006-4
  6. M. Xie and W. Zhang, On the 2k-th mean value formula of general Dedekind sums, (Chinese) Acta Math. Sinica 44 (2001), no. 1, 85-94
  7. T. Zhang and W. Zhang, Hyper Cochrane sums and their hybrid mean value formula (in Chinese), Chinese Ann. Math. Ser. A 26 (2005), no. 4, 469-476
  8. W. Zhang, On the general Dedekind sums and one kind identities of Dirichlet L-functions, Acta Math. Sinica 44 (2001), no. 2, 269-272
  9. W. Zhang, On a Cochrane sum and its hybrid mean value formula, J. Math. Anal. Appl. 267 (2002), no. 1, 89-96 https://doi.org/10.1006/jmaa.2001.7752
  10. W. Zhang, On a Cochrane sum and its hybrid mean value formula II, J. Math. Anal. Appl. 276 (2002), no. 1, 446-457 https://doi.org/10.1016/S0022-247X(02)00501-2
  11. W. Zhang, A sum analogous to Dedekind sums and its hybrid mean value formula, Acta Arith. 107 (2003), no. 1, 1-8 https://doi.org/10.4064/aa107-1-1
  12. W. Zhang and H. Liu, A note on the Cochrane sum and its hybrid mean value formula, J. Math. Anal. Appl. 288 (2003), no. 2, 646-659 https://doi.org/10.1016/j.jmaa.2003.09.056

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  1. A note on the hyper Cochrane sum vol.44, pp.3, 2013, https://doi.org/10.1007/s13226-013-0015-x