Igor Shparlinski

Professor

  • 3984 Citations
  • 27 h-Index
1978 …2019

Research output per year

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Research Outputs

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Article
2019

On functional graphs of quadratic polynomials

Mans, B., Sha, M., Shparlinski, I. E. & Sutantyo, D., 3 Jul 2019, In : Experimental Mathematics. 28, 3, p. 292-300 9 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

On multiplicative dependence of values of rational functions and a generalization of the Northcott theorem

Ostafe, A., Sha, M., Shparlinski, I. E. & Zannier, U., Jun 2019, In : Michigan Mathematical Journal. 68, 2, p. 385-407 23 p.

Research output: Contribution to journalArticle

2 Citations (Scopus)
2018

Arithmetic properties of integers in chains and reflections of g-ary expansions

Gómez-Pérez, D. & Shparlinski, I. E., 2018, In : Experimental Mathematics. 27, 2, p. 184-192 9 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

Effective results on linear dependence for elliptic curves

Sha, M. & Shparlinski, I. E., 2018, In : Pacific Journal of Mathematics. 295, 1, p. 123-144 22 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

On abelian multiplicatively dependent points on a curve in a torus

Ostafe, A., Sha, M., Shparlinski, I. E. & Zannier, U., 1 Jun 2018, In : Quarterly Journal of Mathematics. 69, 2, p. 391-401 11 p.

Research output: Contribution to journalArticle

2 Citations (Scopus)

On multiplicatively dependent vectors of algebraic numbers

Pappalardi, F., Sha, M., Shparlinski, I. E. & Stewart, C. L., Sep 2018, In : Transactions of the American Mathematical Society. 370, 9, p. 6221-6244 24 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

Polynomial interpolation and identity testing from high powers over finite fields

Ivanyos, G., Karpinski, M., Santha, M., Saxena, N. & Shparlinski, I. E., Feb 2018, In : Algorithmica. 80, 2, p. 560-575 16 p.

Research output: Contribution to journalArticle

5 Citations (Scopus)

The Sato–Tate distribution in thin parametric families of elliptic curves

de la Bretèche, R., Sha, M., Shparlinski, I. E. & Voloch, J. F., Dec 2018, In : Mathematische Zeitschrift. 290, 3-4, p. 831-855 25 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)
2017

An explicit polynomial analogue of Romanoff's theorem

Shparlinski, I. E. & Weingartner, A. J., 1 Mar 2017, In : Finite Fields and their Applications. 44, p. 22-33 12 p.

Research output: Contribution to journalArticle

Double exponential sums with exponential functions

Shparlinski, I. E. & Yau, K. H., 2017, In : International Journal of Number Theory. 13, 10, p. 2531-2543 13 p.

Research output: Contribution to journalArticle

3 Citations (Scopus)

Finding elliptic curves with a subgroup of prescribed size

Shparlinski, I. E. & Sutherland, A. V., 1 Feb 2017, In : International Journal of Number Theory. 13, 1, p. 133-152 20 p.

Research output: Contribution to journalArticle

On coincidences among quadratic fields generated by the shanks sequence

Banks, W. D. & Shparlinski, I. E., 1 Jun 2017, In : Quarterly Journal of Mathematics. 68, 2, p. 465-484 20 p.

Research output: Contribution to journalArticle

On distances in lattices from algebraic number fields

Dubickas, A., Sha, M. & Shparlinski, I. E., 2017, In : Moscow Mathematical Journal. 17, 2, p. 239-268 30 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

On the convex hull of the points on multivariate modular hyperbolas

Shparlinski, I. E., 1 Feb 2017, In : Journal of Number Theory. 171, p. 71-78 8 p.

Research output: Contribution to journalArticle

On two functions arising in the study of the Euler and Carmichael quotients

Luca, F., Sha, M. & Shparlinski, I. E., 2017, In : Colloquium Mathematicum. 149, 2, p. 179-192 14 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

Power series approximations to Fekete polynomials

Bell, J. & Shparlinski, I. E., 1 Oct 2017, In : Journal of Approximation Theory. 222, p. 132-142 11 p.

Research output: Contribution to journalArticle

The Sato–Tate distribution in families of elliptic curves with a rational parameter of bounded height

Sha, M. & Shparlinski, I. E., 1 Apr 2017, In : Indagationes Mathematicae. 28, 2, p. 306-320 15 p.

Research output: Contribution to journalArticle

2 Citations (Scopus)
2016

Almost primes of the form ⌊pc

Banks, W. D., Guo, V. Z. & Shparlinski, I. E., 1 Mar 2016, In : Indagationes Mathematicae. 27, 2, p. 423-436 14 p.

Research output: Contribution to journalArticle

4 Citations (Scopus)

Averaging Operators Over Homogeneous Varieties Over Finite Fields

Koh, D., Shen, C. Y. & Shparlinski, I., 1 Apr 2016, In : Journal of Geometric Analysis. 26, 2, p. 1415-1441 27 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

Bounds of double multiplicative character sums and gaps between residues of exponential functions

Shparlinski, I. E. & Yau, K. H., 1 Oct 2016, In : Journal of Number Theory. 167, p. 304-316 13 p.

Research output: Contribution to journalArticle

4 Citations (Scopus)

Cancellations amongst Kloosterman sums

Shparlinski, I. E. & Zhang, T., 2016, In : Acta Arithmetica. 176, 3, p. 201-210 10 p.

Research output: Contribution to journalArticle

12 Citations (Scopus)

Counting Co-cyclic lattices

Nguyen, P. Q. & Shparlinski, I. E., 2016, In : SIAM Journal on Discrete Mathematics. 30, 3, p. 1358-1370 13 p.

Research output: Contribution to journalArticle

2 Citations (Scopus)

Counting irreducible binomials over finite fields

Heyman, R. & Shparlinski, I. E., 1 Mar 2016, In : Finite Fields and their Applications. 38, p. 1-12 12 p.

Research output: Contribution to journalArticle

2 Citations (Scopus)

Cyclotomic coefficients: Gaps and jumps

Camburu, O. M., Ciolan, E. A., Luca, F., Moree, P. & Shparlinski, I. E., 1 Jun 2016, In : Journal of Number Theory. 163, p. 211-237 27 p.

Research output: Contribution to journalArticle

2 Citations (Scopus)

Fractional parts of Dedekind sums

Banks, W. D. & Shparlinski, I. E., 1 Aug 2016, In : International Journal of Number Theory. 12, 5, p. 1137-1147 11 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

Functional graphs of polynomials over finite fields

Konyagin, S. V., Luca, F., Mans, B., Mathieson, L., Sha, M. & Shparlinski, I. E., Jan 2016, In : Journal of Combinatorial Theory. Series B. 116, p. 87-122 36 p.

Research output: Contribution to journalArticle

9 Citations (Scopus)

Groups generated by iterations of polynomials over finite fields

Shparlinski, I. E., Feb 2016, In : Proceedings of the Edinburgh Mathematical Society. 59, 1, p. 235-245 11 p.

Research output: Contribution to journalArticle

4 Citations (Scopus)

Linear congruences with ratios

Shparlinski, I. E., 1 Jul 2016, In : Proceedings of the American Mathematical Society. 144, 7, p. 2837-2846 10 p.

Research output: Contribution to journalArticle

2 Citations (Scopus)

Multiples of squares in short intervals

Rivat, J. & Shparlinski, I. E., 2016, In : Functiones et Approximatio, Commentarii Mathematici. 54, 1, p. 57-63 7 p.

Research output: Contribution to journalArticle

On bilinear exponential and character sums with reciprocals of polynomials

Shparlinski, I. E., 2016, In : Mathematika. 62, 3, p. 842-859 18 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

On Gauss sums and the evaluation of Stechkin's constant

Banks, W. D. & Shparlinski, I. E., 2016, In : Mathematics of Computation. 85, 301, p. 2569-2581 13 p.

Research output: Contribution to journalArticle

On small gaps between the elements of multiplicative subgroups of finite fields

Shparlinski, I. E., 1 Jul 2016, In : Designs, Codes and Cryptography. 80, 1, p. 63-71 9 p.

Research output: Contribution to journalArticle

2 Citations (Scopus)

On the additive energy of the distance set in finite fields

Shparlinski, I. E., Nov 2016, In : Finite Fields and their Applications. 42, p. 187-199 13 p.

Research output: Contribution to journalArticle

On the density of integer points on generalised Markoff–Hurwitz and Dwork hypersurfaces

Chang, M. C. & Shparlinski, I. E., Apr 2016, In : Mathematische Zeitschrift. 282, 3-4, p. 935-954 20 p.

Research output: Contribution to journalArticle

On the singularity of the demjanenko matrix of quotients of fermat curves

Fité, F. & Shparlinski, I. E., 1 Jan 2016, In : Proceedings of the American Mathematical Society. 144, 1, p. 55-63 9 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

Polynomial values in small subgroups of finite fields

Shparlinski, I. E., 2016, In : Revista Matematica Iberoamericana. 32, 4, p. 1127-1136 10 p.

Research output: Contribution to journalArticle

5 Citations (Scopus)

Products of Small Integers in Residue Classes and Additive Properties of Fermat Quotients

Harman, G. & Shparlinski, I. E., 19 Jun 2016, In : International Mathematics Research Notices. 2016, 5, p. 1424-1446 23 p.

Research output: Contribution to journalArticle

12 Citations (Scopus)

Ratios of Small Integers in Multiplicative Subgroups of Residue Rings

Shparlinski, I. E., 2 Jul 2016, In : Experimental Mathematics. 25, 3, p. 273-280 8 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

Systems of congruences with products of variables from short intervals

Shparlinski, I. E., 1 Jun 2016, In : Bulletin of the Australian Mathematical Society. 93, 3, p. 364-371 8 p.

Research output: Contribution to journalArticle

2015

Cayley graphs generated by small degree polynomials over finite fields

Shparlinski, I. E., 2015, In : SIAM Journal on Discrete Mathematics. 29, 1, p. 376-381 6 p.

Research output: Contribution to journalArticle

3 Citations (Scopus)

Character sums and deterministic polynomial root finding in finite fields

Bourgain, J., Konyagin, S. V. & Shparlinski, I. E., 2015, In : Mathematics of Computation. 84, 296, p. 2969-2977 9 p.

Research output: Contribution to journalArticle

5 Citations (Scopus)

Circulant graphs and GCD and LCM of subsets

Von Zur Gathen, J. & Shparlinski, I. E., Feb 2015, In : Information Processing Letters. 115, 2, p. 134-138 5 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

Congruences with intervals and subgroups modulo a prime

Munsch, M. & Shparlinski, I. E., 1 Sep 2015, In : Michigan Mathematical Journal. 64, 3, p. 655-672 18 p.

Research output: Contribution to journalArticle

5 Citations (Scopus)

Counting additive decompositions of quadratic residues in finite fields

Blackburn, S. R., Konyagin, S. V. & Shparlinski, I. E., Jun 2015, In : Functiones et Approximatio, Commentarii Mathematici. 52, 2, p. 223-227 5 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

Distribution of polynomial discriminants modulo a prime

Shparlinski, I. E., Sep 2015, In : Archiv der Mathematik. 105, 3, p. 251-259 9 p.

Research output: Contribution to journalArticle

Explicit form of Cassels' p-adic Embedding Theorem for Number Fields

Dubickas, A., Sha, M. & Shparlinski, I., 1 Oct 2015, In : Canadian Journal of Mathematics. 67, 5, p. 1046-1064 19 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

Lang-trotter and sato-tate distributions in single and double parametric families of elliptic curves

Sha, M. & Shparlinski, I. E., 2015, In : Acta Arithmetica. 170, 4, p. 299-325 27 p.

Research output: Contribution to journalArticle

4 Citations (Scopus)

On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average

Shparlinski, I. E. & Sutherland, A. V., 10 Apr 2015, In : LMS Journal of Computation and Mathematics. 18, 1, p. 308-322 15 p.

Research output: Contribution to journalArticle

4 Citations (Scopus)

On the fixed points of the map x→xx modulo a prime

Kurlberg, P., Luca, F. & Shparlinski, I. E., 2015, In : Mathematical Research Letters. 22, 1, p. 141-168 28 p.

Research output: Contribution to journalArticle

Open Access
4 Citations (Scopus)