An Average Bound for Character Sums with Some Counter-Dependent Recurrence Sequences
Sanka Balasuriya, Igor E. Shparlinski, and Arne Winterhof
Source: Rocky Mountain J. Math. Volume 39, Number 5
(2009), 1403-1409.
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Permanent link to this document: http://projecteuclid.org/euclid.rmjm/1255008567
Digital Object Identifier: doi:10.1216/RMJ-2009-39-5-1403
Zentralblatt MATH identifier: 05614516
Mathematical Reviews number (MathSciNet): MR2546648
References
S. Balasuriya, F. Luca and I.E. Shparlinski, Prime divisors of some recurrence sequence, Period. Math. Hung. 54 (2007), 215-227.
Mathematical Reviews (MathSciNet): MR2337319
Digital Object Identifier: doi:10.1007/s10998-007-4215-4
Zentralblatt MATH: 1174.11001
M.Z. Garaev, F. Luca and I.E. Shparlinski, Character sums and congruences with $n!$, Trans. Amer. Math. Soc. 356 (2004), 5089-5102.
Mathematical Reviews (MathSciNet): MR2084412
Zentralblatt MATH: 1060.11046
Digital Object Identifier: doi:10.1090/S0002-9947-04-03612-8
--------, Exponential sums and congruences with factorials, J. reine Angew. Math. 584 (2005), 29-44.
Mathematical Reviews (MathSciNet): MR2155084
--------, Catalan and Apéry numbers in residue classes, J. Combin. Theory 113 (2006), 851-865.
Mathematical Reviews (MathSciNet): MR2231091
Digital Object Identifier: doi:10.1016/j.jcta.2005.08.003
--------, Exponential sums with Catalan numbers and middle binomial coefficients, Indag. Math. 18 (2007), 23-37.
Mathematical Reviews (MathSciNet): MR2330730
Digital Object Identifier: doi:10.1016/S0019-3577(07)80004-8
Zentralblatt MATH: 1147.11044
R. Lidl and H. Niederreiter, Finite fields, Cambridge University Press, Cambridge, 1997.
Mathematical Reviews (MathSciNet): MR1429394
F. Luca and I. E. Shparlinski, On the square-free parts of $\lfloore n!\rfloor$, Glasgow Math. J. 49 (2007), 411-415.
Mathematical Reviews (MathSciNet): MR2347269
Zentralblatt MATH: 1160.11015
Digital Object Identifier: doi:10.1017/S0017089507003734
T. Müller, Prime and composite terms in Sloane's sequence A056542, J. Integer Sequences 8 (2005), Article 05.3.3.
Mathematical Reviews (MathSciNet): MR2153796
Zentralblatt MATH: 1096.11507
H. Niederreiter and I.E. Shparlinski, On the distribution of power residues and primitive elements in some nonlinear recurring sequences, Bull. London Math. Soc. 35 (2003), 522-528.
Mathematical Reviews (MathSciNet): MR1979007
Zentralblatt MATH: 1055.11010
Digital Object Identifier: doi:10.1112/S002460930300198X
H. Niederreiter and A. Winterhof, Multiplicative character sums of nonlinear recurring sequences, Acta Arithmetica 111 (2004), 299-305.
Mathematical Reviews (MathSciNet): MR2039628
Zentralblatt MATH: 1046.11088
Digital Object Identifier: doi:10.4064/aa111-3-6
W.M. Schmidt, Equations over finite fields, Lecture Notes Math. 536, Springer, Berlin, 1976.
Mathematical Reviews (MathSciNet): MR429733
I.E. Shparlinski, Distribution of nonresidues and primitive roots in recurrent sequences, Mat. Z. 24 (1978), 603-613 (in Russian).
Mathematical Reviews (MathSciNet): MR517420
I.E. Shparlinski and A. Winterhof, On the discrepancy and linear complexity of some counter-dependent recurrence sequences, Lect. Notes Comp. Sci. 4086, Springer-Verlag, Berlin, 2006%), 295--303.
Mathematical Reviews (MathSciNet): MR2444693
Zentralblatt MATH: 1152.94394
Digital Object Identifier: doi:10.1007/11863854_25
N.J.A. Sloane, On-line encyclopedia of integer sequences, available from http://www.research.att.com/~njas/sequences.
I.M. Vinogradov, Elements of number theory, Dover Publications, New York, 1954.
Mathematical Reviews (MathSciNet): MR62138
Zentralblatt MATH: 0057.28201
Rocky Mountain Journal of Mathematics
