By Professor Igor Shparlinski

Journal articles

MULLEN GL; SHPARLINSKI I, 1993, 'VALUES OF LINEAR RECURRING SEQUENCES OF VECTORS OVER FINITE-FIELDS', ACTA ARITHMETICA, 65, pp. 221 - 226, http://dx.doi.org/10.4064/aa-65-3-221-226

Galiev VI; Polupanov AF; Shparlinski IE, 1992, 'Distances from differences of roots of polynomials to the nearest integers', Information Processing Letters, 43, pp. 143 - 146, http://dx.doi.org/10.1016/0020-0190(92)90006-H

Shparlinski IE, 1992, 'A deterministic test for permutation polynomials', Computational Complexity, 2, pp. 129 - 132, http://dx.doi.org/10.1007/BF01202000

Galiev VI; Polupanov AF; Shparlinski IE, 1992, 'On the construction of solutions of systems of linear ordinary differential equations in the neighbourhood of a regular singularity', Journal of Computational and Applied Mathematics, 39, pp. 151 - 163, http://dx.doi.org/10.1016/0377-0427(92)90126-I

Shparlinskiĭ IE, 1992, 'On primitive elements in finite fields and on elliptic curves', Mathematics of the USSR Sbornik, 71, pp. 41 - 50, http://dx.doi.org/10.1070/SM1992v071n01ABEH001389

Stepanov SA; Shparlinskii IE, 1992, 'An estimate of incomplete multiplicative character sum of polynomials', Discrete Mathematics and Applications, 2, pp. 169 - 174, http://dx.doi.org/10.1515/dma.1992.2.2.169

SHPARLINSKI IE; TSFASMAN MA; VLADUT SG, 1992, 'CURVES WITH MANY POINTS AND MULTIPLICATION IN FINITE-FIELDS', LECTURE NOTES IN MATHEMATICS, 1518, pp. 145 - 169, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1992KR02000014&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

SHPARLINSKI IE, 1992, 'ON GAUSSIAN SUMS FOR FINITE-FIELDS AND ELLIPTIC-CURVES', LECTURE NOTES IN COMPUTER SCIENCE, 573, pp. 5 - 15, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1992KQ18400003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Van Der Poorten AJ; Shparlinski IE, 1992, 'On the number of zeros of exponential polynomials and related questions', Bulletin of the Australian Mathematical Society, 46, pp. 401 - 412, http://dx.doi.org/10.1017/S0004972700012065

Shparlinskii IE, 1991, 'Estimates of Gaussian sums', Mathematical Notes of the Academy of Sciences of the USSR, 50, pp. 740 - 746, http://dx.doi.org/10.1007/BF01156612

Shparlinskiy IE, 1991, 'On the Distribution of Values of Recurring Sequences and the Bell Numbers in Finite Fields', European Journal of Combinatorics, 12, pp. 81 - 87, http://dx.doi.org/10.1016/S0195-6698(13)80010-8

Stepanov SA; Shparlinskii IE, 1990, 'On the construction of a primitive normal basis in a finite field', Mathematics of the USSR Sbornik, 67, pp. 527 - 533, http://dx.doi.org/10.1070/SM1990v067n02ABEH001369

Perel'muter GI; Shparlinskii IE, 1990, 'The distribution of primitive roots in finite fields', Russian Mathematical Surveys, 45, pp. 223 - 224, http://dx.doi.org/10.1070/RM1990v045n01ABEH002330

Shparlinskiĭ IE; Skorobogatov AN, 1990, 'Exponential sums and rational points on complete intersections', Mathematika, 37, pp. 201 - 208, http://dx.doi.org/10.1112/S0025579300012912

Shparlinskii IE, 1990, 'Generalization of Chebyshev polynomials', Siberian Mathematical Journal, 31, pp. 183 - 185, http://dx.doi.org/10.1007/BF00971170

Shparlinskii IE, 1990, 'Some arithmetic properties of recurrence sequences', Mathematical Notes of the Academy of Sciences of the USSR, 47, pp. 612 - 617, http://dx.doi.org/10.1007/BF01170895

Shparlinskii IE, 1989, 'On distribution of values of recurrence sequences', Problems of Information Transmission, 25, pp. 120 - 125

Shparlinskii IE, 1989, 'On arithmetical properties of solutions of norm equations', Russian Mathematical Surveys, 44, pp. 216 - 217, http://dx.doi.org/10.1070/RM1989v044n03ABEH002131

Shparlinskiĭ IE, 1989, 'On polynomials of prescribed height in finite fields', Mathematics of the USSR Sbornik, 63, pp. 247 - 255, http://dx.doi.org/10.1070/SM1989v063n01ABEH003271

Shparlinskii IE, 1989, 'Dimension of BCH codes', Problems of Information Transmission, 25, pp. 77 - 80

Shparlinskii IE, 1988, 'Residue classes modulo a prime number in a field of algebraic numbers', Mathematical Notes of the Academy of Sciences of the USSR, 43, pp. 249 - 252, http://dx.doi.org/10.1007/BF01139128

Shparlinskii IE, 1987, 'Number of different prime divisors of recurrence sequences', Mathematical Notes of the Academy of Sciences of the USSR, 42, pp. 773 - 780, http://dx.doi.org/10.1007/BF01138309

Shparlinskii IE, 1986, 'WEIGHT SPECTRA OF SOME CODES.', Problems of Information Transmission, 22, pp. 111 - 116

Shparlinskii IE, 1985, 'Number of prime divisors of recurrence sequences', Mathematical Notes of the Academy of Sciences of the USSR, 38, pp. 529 - 532, http://dx.doi.org/10.1007/BF01137461

Shparlinskii IE, 1985, 'Coefficients of primitive polynomials', Mathematical Notes of the Academy of Sciences of the USSR, 38, pp. 951 - 954, http://dx.doi.org/10.1007/BF01157011

Kosachevskaya LL; Romanovtsev VV; Shparlinskii IE, 1985, 'On one sequence of iteration parameters', USSR Computational Mathematics and Mathematical Physics, 25, pp. 89 - 93, http://dx.doi.org/10.1016/0041-5553(85)90046-1

Shparlinskii IE, 1984, 'Communications of the moscow mathematical society: On the note of convergence of Newton's interpolation process and the power of certain codes', Russian Mathematical Surveys, 39, pp. 199 - 200, http://dx.doi.org/10.1070/RM1984v039n02ABEH003150

Shparlinskii IE, 1984, 'On a multiplicative generator of pseudorandom numbers', USSR Computational Mathematics and Mathematical Physics, 24, pp. 79 - 81, http://dx.doi.org/10.1016/0041-5553(84)90159-9

Kosachevskaya LL; Shparlinskii IE, 1984, 'The rate of convergence of some iterational processes', USSR Computational Mathematics and Mathematical Physics, 24, pp. 81 - 84, http://dx.doi.org/10.1016/0041-5553(84)90088-0

Shparlinskii IE, 1983, 'On one property of a multiplicative transducer of pseudo-random numbers', USSR Computational Mathematics and Mathematical Physics, 23, pp. 158 - 159, http://dx.doi.org/10.1016/S0041-5553(83)80030-5

Kosachevskaya LL; Romanovtsev VV; Shparlinskiy IE, 1983, 'On the spline-based method for experimental data deconvolution', Computer Physics Communications, 29, pp. 227 - 230, http://dx.doi.org/10.1016/0010-4655(83)90002-4

Kosachevskaya LL; Romanovtsev VV; Shparlinskiy IE; Vystavkin AN, 1982, 'New improved algorithm for the iterative solution of a system of linear algebraic equations', Computer Physics Communications, 27, pp. 87 - 89, http://dx.doi.org/10.1016/0010-4655(82)90011-X

Kosachevskaya LL; Romanovtsev VV; Shparlinskii IE, 1982, 'On an iterative process for the numerical solution of systems of linear algebraic equations', USSR Computational Mathematics and Mathematical Physics, 22, pp. 232 - 237, http://dx.doi.org/10.1016/0041-5553(82)90114-8

Shparlinskii IE, 1981, 'The distribution of the fractional parts of recurrent sequences', USSR Computational Mathematics and Mathematical Physics, 21, pp. 231 - 235, http://dx.doi.org/10.1016/0041-5553(81)90169-5

Levin MB; Shparlinskii IE, 1979, 'The uniform distribution of fractional parts of recurrent sequences', Russian Mathematical Surveys, 34, pp. 207 - 208, http://dx.doi.org/10.1070/RM1979v034n03ABEH003995

Shparlinskii IE, 1979, 'On a completely uniform distribution', USSR Computational Mathematics and Mathematical Physics, 19, pp. 249 - 253, http://dx.doi.org/10.1016/0041-5553(79)90117-4

Shparlinskii IE, 1978, 'Distribution of nonresidues and primitive roots in recurrent sequences', Mathematical Notes of the Academy of Sciences of the USSR, 24, pp. 823 - 828, http://dx.doi.org/10.1007/BF01141537

Conference Papers

Kaminski M; Shparlinski IE, 2021, 'Sets of Linear Forms Which Are Hard to Compute', in Leibniz International Proceedings in Informatics Lipics, http://dx.doi.org/10.4230/LIPIcs.MFCS.2021.66

Shparlinski I; Childs AM; van Dam W, 2016, 'Optimal Quantum Algorithm for Polynomial Interpolation', in Ioannis Chatzigiannakis MMYRADS (ed.), Proceedings of the 43rd International Colloquium on Automata, Languages, and Programming, DROPS, Rome, pp. 16:1 - 16:13, presented at 43rd International Colloquium on Automata, Languages, and Programming, Rome, 11 July 2016 - 15 July 2016, http://dx.doi.org/10.4230/lipics.icalp.2016.16

Shparlinski IE, 2016, 'Dynamical systems of non-algebraic origin: Fixed points and orbit lengths', pp. 261 - 283, http://dx.doi.org/10.1090/conm/669/13432

Kohel D; Shparlinski I, 2016, 'Preface', in Contemporary Mathematics, pp. vii - viii

Shparlinski IE, 2008, 'OPEN PROBLEMS ON EXPONENTIAL AND CHARACTER SUMS', in Aoki T; Kanemitsu S; Liu JY (eds.), NUMBER THEORY: DREAMING IN DREAMS, WORLD SCIENTIFIC PUBL CO PTE LTD, JAPAN, Kinki Univ, Higashiosaka, pp. 222 - 242, presented at 5th China-Japan Seminar on Number Theory, JAPAN, Kinki Univ, Higashiosaka, 27 August 2008 - 31 August 2008, http://dx.doi.org/10.1142/9789814289924_0010

Shparlinski IE, 2008, 'Pseudorandom Points on Elliptic Curves over Finite Fields', in Algebraic Geometry and Its Applications, WORLD SCIENTIFIC, pp. 116 - 134, presented at Proceedings of the First SAGA Conference, http://dx.doi.org/10.1142/9789812793430_0006

Luca F; Shparlinski IE, 2007, 'On Special Finite Fields', in Lachaud G; Ritzenthaler C; Tsfasman MA (eds.), ARITHMETIC, GEOMETRY, CRYPTOGRAPHY AND CODING THEORY, AMER MATHEMATICAL SOC, FRANCE, Ctr Int Rencontres Math, Marseilles, pp. 163 - 167, presented at 11th Conference on Arithmetic, Geometry, Cryptography and Coding Theory, FRANCE, Ctr Int Rencontres Math, Marseilles, 05 November 2007 - 09 November 2007, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000267679700010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

EI-Mahassni E; Shparlinski IE, 2007, 'On the distribution of the elliptic curve power generator', in Mullen GL; Panario D; Shparlinski IE (eds.), FINITE FIELDS AND APPLICATIONS, AMER MATHEMATICAL SOC, AUSTRALIA, Melbourne, pp. 111 - 118, presented at 8th International Conference on Finite Fields and Applications, AUSTRALIA, Melbourne, 09 July 2007 - 13 July 2007, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000257880200009&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Shparlinski IE; Steinfeld R, 2007, 'Collision in the DSA Function', in Li Y; Ling S; Niederreiter H; Wang H; Xing C; Zhang S (eds.), CODING AND CRYPTOLOGY, WORLD SCIENTIFIC PUBL CO PTE LTD, PEOPLES R CHINA, Fujian Normal Univ, Wuui Mt, pp. 226 - 232, presented at 1st International Workshop on Coding and Cryptology, PEOPLES R CHINA, Fujian Normal Univ, Wuui Mt, 11 June 2007 - 15 June 2007, http://dx.doi.org/10.1142/9789812832245_0017

Shparlinski IE, 2006, 'DISTRIBUTION OF POINTS ON MODULAR HYPERBOLAS', in Kanemitsu S; Liu JY (ed.), NUMBER THEORY: SAILING ON THE SEA OF NUMBER THEORY, WORLD SCIENTIFIC PUBL CO PTE LTD, PEOPLES R CHINA, Weihai, pp. 155 - 189, presented at 4th China-Japan Seminar on Number Theory, PEOPLES R CHINA, Weihai, 30 August 2006 - 03 September 2006, http://dx.doi.org/10.1142/9789812770134_0007

Shparlinski IE, 2006, 'Bounds on the Fourier Coefficients of the Weighted Sum Function', in Dagstuhl Seminar Proceedings

Shparlinski IE, 2005, 'Pseudorandom Number Generators from Elliptic Curves', in Luengo I (ed.), RECENT TRENDS IN CRYPTOGRAPHY, AMER MATHEMATICAL SOC, SPAIN, Real Soc Mat Espanola, Santander, pp. 121 - 141, presented at Summer School on Recent Trends in Cryptography, SPAIN, Real Soc Mat Espanola, Santander, 11 July 2005 - 15 July 2005, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000263678500005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Shparlinski IE, 2003, 'Orders of points on elliptic curves', in Gutierrez J; Shpilrain V; Yu JT (eds.), AFFINE ALGEBRAIC GEOMETRY, AMER MATHEMATICAL SOC, SPAIN, Seville, pp. 245 - 251, presented at 1st RSME-AMS Joint Meeting, SPAIN, Seville, 19 June 2003 - 21 June 2003, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000227464800015&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Back to profile page