Igor E. Shparlinski

Algebra and Number Theory · 2000–2018

A researcher in the Science corpus: 21 papers; trusts 31 researchers and is trusted by 12 researchers here, as inferred from the citation graph.

Subfields

• Algebra and Number Theory — 34 citations into it; #1,439 of 2,864 by trust here, #902 by citations
• Geometry and Topology — 34 citations into it; #2,646 of 7,422 by trust here, #5,008 by citations
• Discrete Mathematics and Combinatorics — 22 citations into it; #676 of 2,017 by trust here, #370 by citations
• Mathematical Physics — 16 citations into it; #6,252 of 8,562 by trust here, #5,794 by citations
• Computational Theory and Mathematics — 12 citations into it
• Applied Mathematics — 10 citations into it
• Artificial Intelligence — 10 citations into it; #19,208 of 35,345 by trust here, #19,439 by citations
• Statistical and Nonlinear Physics — 6 citations into it

Whom Igor E. Shparlinski trusts overall

Their strongest outbound trust, strongest first, inferred from their citations.

1. Jean Bourgain
2. Kevin Ford
3. Alina Carmen Cojocaru
4. Javier Cilleruelo
5. Moubariz Z. Garaev
6. Ivan Gutman
7. John B. Friedlander
8. Kannan Soundararajan
9. 'Etienne Fouvry
10. Chris Hall

Who trusts Igor E. Shparlinski overall

1. Richard A. Brualdi
2. Vladimir Nikiforov
3. Gopalapillai Indulal
4. Tanja Lange
5. Antal Balog
6. Jean Bourgain

Papers from Igor E. Shparlinski's perspective

Ordered by how strongly the researchers Igor E. Shparlinski trusts endorse each paper. Same corpus, a different order for every researcher.

1. Concentration of Points on Two and Three Dimensional Modular Hyperbolas and Applications
2. Analytic Number Theory (All the Math You Missed)
3. New bounds for Gauss sums derived from kth powers
4. Quasi-Monte Carlo methods and pseudo-random numbers
5. Product Sets of Rationals, Multiplicative Translates of Subgroups in Residue Rings, and Fixed Points of the Discrete Logarithm
6. MORE ON THE SUM-PRODUCT PHENOMENON IN PRIME FIELDS AND ITS APPLICATIONS
7. On the statistical properties of Diffie-Hellman distributions
8. Estimates for the number of sums and products and for exponential sums over subgroups in fields of prime order
9. The distribution of integers with a divisor in a given interval
10. Additive Theory of Prime Numbers

Their papers

• Recurrence Sequences (2003) — 353 citations
• Character sums with exponential functions (2000) — 80 citations
• On a sum involving the Euler function (2018) — 59 citations
• On the concentration of points of polynomial maps and applications (2012) — 53 citations
• Piatetski-Shapiro sequences (2012) — 51 citations
• On congruences with products of variables from short intervals and applications (2012) — 48 citations
• Modular hyperbolas (2011) — 65 citations
• Product Sets of Rationals, Multiplicative Translates of Subgroups in Residue Rings, and Fixed Points of the Discrete Logarithm (2010) — 57 citations
• On the Divisibility of Fermat Quotients (2010) — 52 citations
• Graphs with integral spectrum (2009) — 104 citations
• Pseudoprime reductions of elliptic curves (2009) — 54 citations
• Prime numbers with Beatty sequences (2007) — 50 citations
• Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height (2006) — 54 citations
• On the energy of some circulant graphs (2006) — 58 citations
• Certain Exponential Sums and Random Walks on Elliptic Curves (2005) — 58 citations
• On the average value of divisor sums in arithmetic progressions (2005) — 53 citations
• On the cycle structure of repeated exponentiation modulo a prime (2004) — 68 citations
• Elliptic divisibility sequences (2003) — 70 citations
• Some doubly exponential sums over Z[m] (2002) — 54 citations
• Recent Advances in the Theory of Nonlinear Pseudorandom Number Generators (2002) — 72 citations