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# 周文賢

 周文賢從輔仁大學數學系和數學研究所 分別獲得學士和碩士學位, 服完兵役後,在國內 教了六年的書, 由於自覺有所不足, 於一九八四年 赴美進修, 先在南伊大唸了兩年, 其後轉學至賓州 州立大學。並在那裡得到博士學位。於一九九０年 六月到本所服務, 現為研究員。其主要領域為 有限體理論及其在各方面的應用。 Email : macws AT math.sinica.edu.tw Phone:+886 2 2368-5999 ext. 709 Fax: +886 2 2368-9771

### 著作目錄 :

 1 (with A. Blokhuis, X. Cao and X.-D. Hou) On the Roots of Certain Dickson Polynomials, (2018) 2 (with X. Cao and X. Zhang) More constructions of near optimal codebooks associated with binary sequences, Advances in Mathematics of Communications , 11(2017-02), no. 1, 187-202 3 (with X. Cao, J. Gu) On the number of solutions of certain diagonal equations over finite fields, FINITE FIELDS AND THEIR APPLICATIONS , 42(2016), 225-252 4 (with Cao X.) More Constructions of Approximately Mutually Unbiased Bases, Bulletin of the Australian Mathematical Society , 93(2016), 211-222 5 (with Hsu L. C.) An Extension of Fleck-type M$\ddot{\mbox{o}}$bius Function and Inversion, International Journal Of Number Theory , 11(2015), no. 6, 1807-1819 6 (with He T.-X., Shiue P. J.-S.) Enumeration problems for a linear congruence equation, Taiwanese Journal of Mathematics , 18(2014-02), no. 1, 265-275 7 (with He T.-X.) On the construction of number sequence identities, J. Concrete and Appl. Math. , 11(2013), 277-291 8 (with J. Gomez-Calderon, G. L. Mullen, D. Panario, D. Thomson) Subfield value sets of polynomials over finite fields, Functiones et Approximatio Commentarii Mathematici , 48(2013), no. 1, 147-165 9 (with G.L. Mullen! B. Wassermann) On the number of solutions of equations of Dickson polynomials over finite fields, NSC94-2115-M-001-019, Taiwanese Journal of Mathematics , 12(2008), 917-931 10 (with B.-S. Du ! P.J.-S.Shiue) A note on circulant transition matrices in Markov chains, NSC94-2115-M-001-019, Linear Algebra and Its Applications , 429(2008), 1699-1704 11 (with L.C.Hsu!P.J.-S.Shiue) On a class of combinatorial sums involving generalized factorials, doi:10.1155/2007/12604, Int. J. Math. & Math. Sciences (2007), 0-0 12 (with P. J.-S. Shiue) Periodic aspects of sequences generated by two special mappings, Taiwanese J. Math. , 10(2006), no. 4, 829-836 13 (with L. C. Hsu ! P. J.-S. Shiue) Application of Faa di Bruno's formula in characterization of inverse relations, J. Comput. Applied Math , 190(2006), 151-169 14 Binomial permutations of finite fields, Bull. Austral. Math. Soc. , 38(1988), 325-327 15 (with J. Gomez-Calderon and G. L. Mullen) Value sets of Dickson polynomials over finite fields, J. Number Theory , 30(1988), 334-344 16 (with G. L. Mullen, P. J.-S. Shiue, and Q. Sun) Pairs of primitive elements modulo $p^l$, J. Sichuan Univ. Natural Science , 26(1989), 189-195 17 Permutation Polynomials on Finite Fields and Combinatorial Applications, Ph.D. thesis, Penn. State University (1990) 18 (with H. Bowman and P. J.-S. Shiue) A matrix method for solving the postage stamps problem, Missouri J. Math. Sciences , 2(1991), 70-76 19 Formulas for counting chains in multisets, Utilitas Math. , 40(1991), 3-12 20 (with G. L. Mullen) Generating linear spans over finite fields, Acta Arith. , 61(1992), 183-191 21 Set-complete mappings on finite fields, Finite Fields, Coding Theory, and Advances in Communications and Computing (Las Vegas, 1991), Lecture Notes in Pure and Appl. Math., vol. 141, pp. 33--41, Dekker, New York, 1993., (1993) 22 (with P. J.-S. Shiue) A note on circular permutations, J. Comb. Math. Combl. Comp. , 16(1994), 165-170 23 (with Y. Manoussakis, O. Megalakaki, M. Spylatos, and Zs. Tuza) Paths through fixed vertices in edge-colored graphs, Math. Inf. Sci. Hum. (1994), 49-58 24 The period lengths of inversive pseudorandom vector generations, Finite Fields & Their Appls. , 1(1995), 126-132 25 On inversive maximal period polynomials over finite fields, Applicable Algebra in Engrg. Comm. Comp. , 6(1995), 245-250 26 The period lengths of inversive congruential recursions, Acta Arith. , 73(1995), 325-341 27 (with H. Niederreiter) On the lattice test for inversive congruential pseudorandom numbers, Monte Carlo & Quasi-Monte Carlo Methods in Scientific Computing (Las Vegas, 1994), Lecture Notes in Statistics, vol.~106, pp.~186--197, Springer-Verlag, New York, 1995, (1995) 28 The factorization of Dickson polynomials over finite fields, Finite Fields & Their Appls. , 3(1997), 84-96 29 (with J.-M. Ku and P. J.-S. Shiue) On crossings of hyperplanes on the n-D torus, J. Algebra , 192(1997), 43-54 30 (with S. D. Cohen) Polynomial distribution and sequences of irreducible polynomoials over finite finite fields, J. Number Theory , 75(1999), 145-159 31 (with P. J.-S. Shiue) crossings on the 2-D torus, ARS Combinatorica , 54(2000), 29-31 32 (with S. D. Cohen) Primitive elements with zero traces. NSC88-2115-M-001-002, Finite Field & Their Appls. , 7(2001), 125-141 33 (with H. Niederreiter) Monomials and binomials over finite fields as $\scr R$-orthomorphisms. NSC88-2115-M-001-002, Publ. Math. Debcreen , 61(2002), 511-521 34 (with T. C. Brown and P. J.-S. Shiue) On the partition function of a finite set, Australasian J. Comb. , 27(2003), 193-204 35 (with I. E. Shparlinski) On the cycle structure of repeated exponentiation modulo a prime. NSC92-2115-M-001-026, J. Number Theory , 107(2004), 345-356 36 (with Y. Chang and P. J.-S. Shiue) On the number of primitive polynomials over finite fields, Finite Fields & Their Appls. , 11(2005), 156-163