Number Theory, Analysis, and Combinatorics

Proceedings of the Paul Turan Memorial Conference held August 22-26, 2011 in Budapest

János Pintz, András Biró, Kálmán Györy, Gergely Harcos, Miklós Simonovits, József Szabados, János Pintz, András Biró, Kálmán Györy, Gergely Harcos, Miklós Simonovits, József Szabados

• Publisher: De Gruyter
• Year: 2013
• Print ISBN: 9783110282375
• eBook ISBN: 9783110282429
• Edition: 1
• Topic: Mathematics
• Subtopic: Counting & Numeration
• Index: Mathematics

Paul Turán, one of the greatest Hungarian mathematicians, was born 100 years ago, on August 18, 1910. To celebrate this occasion the Hungarian Academy of Sciences, the Alfréd Rényi Institute of Mathematics, the János Bolyai Mathematical Society and the Mathematical Institute of Eötvös Loránd University organized an international conference devoted to Paul Turán's main areas of interest: number theory, selected branches of analysis, and selected branches of combinatorics.

The conference was held in Budapest, August 22-26, 2011. Some of the invited lectures reviewed different aspects of Paul Turán's work and influence. Most of the lectures allowed participants to report about their own work in the above mentioned areas of mathematics.

Table of contents

• Preface
• List of contributing authors
• Random union-closed families
• Small populations of zeros of L-functions
• Turá¡n-type inequalities and the distribution of zeros of entire functions
• Paul Turá¡n and Probabilistic Number Theory
• Effective results for Diophantine equations over finitely generated domains: A survey
• On the optimal weight function in the Goldston–Pintz–Yıldırım method for finding small gaps between consecutive primes
• Untangling upper-bound sieves
• On a theorem of Erdős and Simonovits on graphs not containing the cube
• A survey of Turán’s equivalent power series
• Internal twists of L-functions
• Turán’s new method and compressive sampling
• Turán’s graph theorem, measures and probability theory
• On the Turán–Kubilius inequality
• Sums of a smooth number and a number with missing digits
• Turán’swork in analytic number theory
• On the irreducibility of basic automorphic representations
• On composite rational functions
• Some new results on gaps between consecutive primes
• On some results of Turán about the local behavior of polynomials
• On multiplicative decompositions of the set of the shifted quadratic residues modulo p
• Paul Turán’s influence in combinatorics
• On optimal interpolatory point systems
• Paul Turán – A Capsule Biography