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| András Sárközy | |
|---|---|
| Name | András Sárközy |
| Birth date | 1939 |
| Birth place | Székesfehérvár, Hungary |
| Nationality | Hungarian |
| Fields | Number theory, Combinatorics |
| Institutions | Alfréd Rényi Institute of Mathematics, Eötvös Loránd University |
| Alma mater | Eötvös Loránd University |
| Doctoral advisor | Pál Erdős |
András Sárközy is a Hungarian mathematician known for contributions to additive number theory, combinatorial number theory, and analytic methods in arithmetic. He produced influential results on additive bases, difference sets, sum-free subsets, and the distribution of arithmetic functions, collaborating with leading figures and shaping subsequent research in probabilistic and combinatorial aspects of number theory. His work spans problems connected to the names of Paul Erdős, Paul Turán, Alfréd Rényi, Pál Turán, and institutions such as the Alfréd Rényi Institute of Mathematics and Eötvös Loránd University.
Born in Székesfehérvár, Hungary, he completed secondary studies before entering higher education at Eötvös Loránd University, where he studied under advisors linked to the Hungarian school of mathematics. His doctoral studies connected him with networks centered on Paul Erdős, Alfréd Rényi, and the mathematical community in Budapest. During formative years he engaged with problems influenced by classical results of Ivan Vinogradov, G. H. Hardy, John Littlewood, and later developments by Atle Selberg and Erdős–Turán problems in additive number theory.
He held positions at the Alfréd Rényi Institute of Mathematics and Eötvös Loránd University, participating in seminars alongside researchers from the Hungarian Academy of Sciences and collaborating with contemporaries such as Paul Erdős, Imre Z. Ruzsa, József Beck, and Endre Szemerédi. Visiting appointments and lectures took him to institutions including University of Cambridge, Princeton University, Institute for Advanced Study, University of Illinois Urbana–Champaign, and research centers like Mathematical Institute of the Hungarian Academy of Sciences. He served on editorial boards for journals associated with the London Mathematical Society, American Mathematical Society, and regional publications in Central Europe.
Sárközy made seminal advances in additive and combinatorial number theory, addressing problems connected to difference sets, polynomial configurations in sets of integers, and gaps between special sequences. He proved results related to polynomial patterns avoiding long arithmetic progressions, building on techniques from Paul Erdős, Pál Erdős–Turán conjecture-style questions, and methods influenced by Hardy–Littlewood circle method, Vinogradov's methods, and sieve techniques of Atle Selberg.
Key contributions include work on sum-free sets, sets without k-term arithmetic progressions, and on the structure of difference sets in dense subsets of integers; these results interact with theorems and conjectures by Van der Waerden, Szemerédi's theorem, Behrend constructions, and the probabilistic combinatorics methods promoted by Béla Bollobás and Alfréd Rényi. He established bounds and density results for sequences lacking polynomial differences, relating to the Sárközy theorem class of results connecting polynomial values and difference sets. His techniques combined Fourier analytic tools, exponential sum estimates, and combinatorial constructions reminiscent of work by János Komlós, Miklós Simonovits, and Endre Szemerédi.
Sárközy's papers tackled distribution questions for arithmetic functions, refining error terms in additive problems akin to investigations by G. H. Hardy, Nikolai Korobov, and I. M. Vinogradov. Collaborative papers addressed interdisciplinary connections with graph theory concepts developed by Paul Erdős and Rényi, and with probabilistic methods used by Persi Diaconis and Joel Spencer.
He received recognition from Hungarian and international mathematical communities, including membership and fellowships affiliated with the Hungarian Academy of Sciences and awards honoring lifetime achievement in number theory and combinatorics. His collaborations with Paul Erdős placed him among a network of mathematicians celebrated in commemorative conferences and volumes organized by institutions such as the Alfréd Rényi Institute of Mathematics and universities in Budapest, Cambridge, and Princeton. Festschrifts and dedicated sessions at meetings of the American Mathematical Society and the European Mathematical Society have acknowledged his influence.
- "On difference sets of sequences of integers" — papers addressing polynomial differences, appearing in journals associated with the Hungarian Academy of Sciences and international periodicals influenced by editorial boards of the AMS and LMS. - Collaborative works with Paul Erdős on additive problems and combinatorial constructions, published in venues connected to the Journal of Number Theory and proceedings of conferences at Eötvös Loránd University. - Articles developing bounds for sets avoiding polynomial configurations, engaging methods from the Hardy–Littlewood circle method, exponential sum techniques of Vinogradov, and probabilistic combinatorics popularized by Joel Spencer and Béla Bollobás.
Sárközy's results influenced subsequent work by researchers such as Imre Z. Ruzsa, József Beck, Endre Szemerédi, Béla Bollobás, and younger scholars at the Alfréd Rényi Institute of Mathematics and Eötvös Loránd University. His theorems on polynomial differences and sum-free structures became tools in later advances on Szemerédi's theorem refinements, polynomial extensions of additive combinatorics, and probabilistic number theory. The methods he used — blending analytic number theory with combinatorial constructions — continue to appear in contemporary research related to additive bases, the study of pseudorandomness in arithmetic sets, and connections between arithmetic combinatorics and theoretical computer science problems addressed by researchers at institutions like MIT, Stanford University, and Princeton University.
Category:Hungarian mathematicians