2019

Cohen, S. D. and Trudgian, T. (2019) Lehmer numbers and primitive roots modulo a prime. Journal of Number Theory, 203, pp. 68-79. (doi: 10.1016/j.jnt.2019.03.004)

2015

Cohen, S. D., Oliveira e Silva, T. and Trudgian, T. (2015) A proof of the conjecture of Cohen and Mullen on sums of primitive roots. Mathematics of Computation, 84(296), pp. 2979-2986. (doi: 10.1090/mcom/2950)

2014

Cohen, S. D. (2014) Pairs of primitive elements in fields of even order. Finite Fields and their Applications, 28, pp. 22-42. (doi: 10.1016/j.ffa.2014.01.012)

2010

Cohen, S.D. (2010) Primitive elements on lines in extensions of finite fields. In: McGuire, G., Mullen, G.L., Panario, D. and Shparlinski, I.E. (eds.) Finite Fields: Theory and Applications. Series: Contemporary Mathematics (518). American Mathematical Society: Providence, RI, pp. 113-127. ISBN 978-0-8218-4786-2

Cohen, S.D. and Huczynska, S. (2010) The strong primitive normal basis theorem. Acta Arithmetica, 143(4), pp. 299-332. (doi: 10.4064/aa143-4-1)

2008

Cohen, S.D. and Presern, M. (2008) The Hansen-Mullen primitivity conjecture: completion of proof. In: McKee, J. and Smyth, C. (eds.) Number Theory and Polynomials. Series: London Mathematical Society lecture note series (352). Cambridge University Press: Cambridge, UK. ISBN 9780521714679

2006

Cohen, S.D. (2006) Primitive polynomials with a prescribed coefficient. Finite Fields and their Applications, 12(3), pp. 425-491. (doi: 10.1016/j.ffa.2005.08.001)

Cohen, S.D. and Presern, M. (2006) Primitive polynomials with prescribed second coefficient. Glasgow Mathematical Journal, 48(2), pp. 281-307. (doi: 10.1017/S0017089506003077)

2005

Arora, S.K., Batra, S. and Cohen, S. (2005) The primitive idempotents of a cyclic group algebra, II. Southeast Asian Bulletin of Mathematics, 29(2), pp. 197-208.

Cohen, S. and Presern, M. (2005) Primitive finite field elements with prescribed trace. Southeast Asian Bulletin of Mathematics, 29(2), pp. 283-300.

Cohen, S. (2005) Explicit theorems on generator polynomials. Finite Fields and their Applications, 11, pp. 337-357. (doi: 10.1016/j.ffa.2005.05.002)

Cohen, S. (2005) Finite field elements with specified order and traces. Designs Codes and Cryptography, 36, pp. 331-340. (doi: 10.1007/s10623-004-1724-2)

Cohen, S., Dewar, M., Friedlander, J., Panario, D. and Shparlinski, I. (2005) Polynomial Gauss sums. Proceedings of the American Mathematical Society, 133, pp. 2225-2231.

2004

Cohen, S. and King, C. (2004) The three fixed coefficient primitive polynomial theorem. Journal of Algebra, Number Theory and Applications, 4(1), pp. 79-87.

Cohen, S. (2004) Primitive polynomials over small fields. Finite Fields and their Applications, 2948, pp. 197-214.

Franken, R. and Cohen, S. (2004) The covering radius of some primitive ternary BCH codes. Finite Fields and their Applications, 2948, pp. 166-180.

2003

Cohen, S. (2003) Obituary: Robert Winston Keith Odoni (1947-2002). Glasgow Mathematical Journal, 45(3), pp. 569-575. (doi: 10.1017/S0017089503001472)

Cohen, S.D. and Huczynska, S. (2003) The primitive normal basis theorem without a computer. Journal of the London Mathematical Society: Second Series, 67, pp. 41-56. (doi: 10.1112/S0024610702003782)

Cohen, S. (2003) The orders of related elements of a finite field. Ramanujan Journal, 7, pp. 169-183.

Cohen, S. and Huczynska, S. (2003) Primitive free quartics with specified norm and trace. Acta Arithmetica, 109, pp. 359-385.

Cohen, S. and Mills, D. (2003) Primitive polynomials with first and second coefficients prescribed. Finite Fields and their Applications, 9, pp. 334-350. (doi: 10.1016/S1071-5797(03)00009-1)

Huczynska, S. and Cohen, S.D. (2003) Primitive free cubics with specified norm and trace. Transactions of the American Mathematical Society, 355(8), pp. 3099-3116. (doi: 10.1090/S0002-9947-03-03301-4)

2002

Arora, S.K., Batra, S., Cohen, S. and Pruthi, M. (2002) The primitive idempotents of a cyclic group algebra. Southeast Asian Bulletin of Mathematics, 26(4), pp. 549-557. (doi: 10.1007/s100120200058)

Cohen, S. and Zhang, W. (2002) Sums of two exact powers. Finite Fields and their Applications, 8, pp. 471-477. (doi: 10.1006/ffta.2001.0354)

2001

Chou, W. and Cohen, S. (2001) Primitive elements with zero traces. Finite Fields and their Applications, 7, pp. 125-141. (doi: 10.1006/ffta.2000.0284)

Cohen, S. (2001) A permutation of a small infinite field. In: Jungnickel, D. and Niederreiter, H. (eds.) Finite Fields and Applications. Springer, pp. 109-112. ISBN 3540411097

Cohen, S., Niederreiter, H., Shparlinski, I.E. and Zieve, M. (2001) Incomplete character sums and a special class of permutations. Journal de Théorie des Nombres de Bordeaux, 13(1), pp. 53-63. (doi: 10.5802/jtnb.303)

Articles

Cohen, S. D. and Trudgian, T. (2019) Lehmer numbers and primitive roots modulo a prime. Journal of Number Theory, 203, pp. 68-79. (doi: 10.1016/j.jnt.2019.03.004)

Cohen, S. D., Oliveira e Silva, T. and Trudgian, T. (2015) A proof of the conjecture of Cohen and Mullen on sums of primitive roots. Mathematics of Computation, 84(296), pp. 2979-2986. (doi: 10.1090/mcom/2950)

Cohen, S. D. (2014) Pairs of primitive elements in fields of even order. Finite Fields and their Applications, 28, pp. 22-42. (doi: 10.1016/j.ffa.2014.01.012)

Cohen, S.D. and Huczynska, S. (2010) The strong primitive normal basis theorem. Acta Arithmetica, 143(4), pp. 299-332. (doi: 10.4064/aa143-4-1)

Cohen, S.D. (2006) Primitive polynomials with a prescribed coefficient. Finite Fields and their Applications, 12(3), pp. 425-491. (doi: 10.1016/j.ffa.2005.08.001)

Cohen, S.D. and Presern, M. (2006) Primitive polynomials with prescribed second coefficient. Glasgow Mathematical Journal, 48(2), pp. 281-307. (doi: 10.1017/S0017089506003077)

Arora, S.K., Batra, S. and Cohen, S. (2005) The primitive idempotents of a cyclic group algebra, II. Southeast Asian Bulletin of Mathematics, 29(2), pp. 197-208.

Cohen, S. and Presern, M. (2005) Primitive finite field elements with prescribed trace. Southeast Asian Bulletin of Mathematics, 29(2), pp. 283-300.

Cohen, S. (2005) Explicit theorems on generator polynomials. Finite Fields and their Applications, 11, pp. 337-357. (doi: 10.1016/j.ffa.2005.05.002)

Cohen, S. (2005) Finite field elements with specified order and traces. Designs Codes and Cryptography, 36, pp. 331-340. (doi: 10.1007/s10623-004-1724-2)

Cohen, S., Dewar, M., Friedlander, J., Panario, D. and Shparlinski, I. (2005) Polynomial Gauss sums. Proceedings of the American Mathematical Society, 133, pp. 2225-2231.

Cohen, S. and King, C. (2004) The three fixed coefficient primitive polynomial theorem. Journal of Algebra, Number Theory and Applications, 4(1), pp. 79-87.

Cohen, S. (2004) Primitive polynomials over small fields. Finite Fields and their Applications, 2948, pp. 197-214.

Franken, R. and Cohen, S. (2004) The covering radius of some primitive ternary BCH codes. Finite Fields and their Applications, 2948, pp. 166-180.

Cohen, S. (2003) Obituary: Robert Winston Keith Odoni (1947-2002). Glasgow Mathematical Journal, 45(3), pp. 569-575. (doi: 10.1017/S0017089503001472)

Cohen, S.D. and Huczynska, S. (2003) The primitive normal basis theorem without a computer. Journal of the London Mathematical Society: Second Series, 67, pp. 41-56. (doi: 10.1112/S0024610702003782)

Cohen, S. (2003) The orders of related elements of a finite field. Ramanujan Journal, 7, pp. 169-183.

Cohen, S. and Huczynska, S. (2003) Primitive free quartics with specified norm and trace. Acta Arithmetica, 109, pp. 359-385.

Cohen, S. and Mills, D. (2003) Primitive polynomials with first and second coefficients prescribed. Finite Fields and their Applications, 9, pp. 334-350. (doi: 10.1016/S1071-5797(03)00009-1)

Huczynska, S. and Cohen, S.D. (2003) Primitive free cubics with specified norm and trace. Transactions of the American Mathematical Society, 355(8), pp. 3099-3116. (doi: 10.1090/S0002-9947-03-03301-4)

Arora, S.K., Batra, S., Cohen, S. and Pruthi, M. (2002) The primitive idempotents of a cyclic group algebra. Southeast Asian Bulletin of Mathematics, 26(4), pp. 549-557. (doi: 10.1007/s100120200058)

Cohen, S. and Zhang, W. (2002) Sums of two exact powers. Finite Fields and their Applications, 8, pp. 471-477. (doi: 10.1006/ffta.2001.0354)

Chou, W. and Cohen, S. (2001) Primitive elements with zero traces. Finite Fields and their Applications, 7, pp. 125-141. (doi: 10.1006/ffta.2000.0284)

Cohen, S., Niederreiter, H., Shparlinski, I.E. and Zieve, M. (2001) Incomplete character sums and a special class of permutations. Journal de Théorie des Nombres de Bordeaux, 13(1), pp. 53-63. (doi: 10.5802/jtnb.303)

Book Sections

Cohen, S.D. (2010) Primitive elements on lines in extensions of finite fields. In: McGuire, G., Mullen, G.L., Panario, D. and Shparlinski, I.E. (eds.) Finite Fields: Theory and Applications. Series: Contemporary Mathematics (518). American Mathematical Society: Providence, RI, pp. 113-127. ISBN 978-0-8218-4786-2

Cohen, S.D. and Presern, M. (2008) The Hansen-Mullen primitivity conjecture: completion of proof. In: McKee, J. and Smyth, C. (eds.) Number Theory and Polynomials. Series: London Mathematical Society lecture note series (352). Cambridge University Press: Cambridge, UK. ISBN 9780521714679

Cohen, S. (2001) A permutation of a small infinite field. In: Jungnickel, D. and Niederreiter, H. (eds.) Finite Fields and Applications. Springer, pp. 109-112. ISBN 3540411097