Melvyn B. Nathanson 
Combinatorial and Additive Number Theory IV 
CANT, New York, USA, 2019 and 2020

This is the fourth in a series of proceedings of the Combinatorial and Additive Number Theory (CANT) conferences, based on talks from the 2019 and 2020 workshops at the City University of New York. The latter was held online due to the COVID-19 pandemic, and featured speakers from North and South America,  Europe, and Asia. The 2020 Zoom conference was the largest CANT conference in terms of the number of both lectures and participants.





These proceedings contain 25 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003 at the CUNY Graduate Center,  the workshop surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Topics featured in this volume include sumsets, zero-sum sequences, minimal complements, analytic and prime number theory, Hausdorff dimension, combinatorial and discrete geometry, and Ramsey theory. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.

Table des matières

0. Math in the Time of Covid (M.B. Nathanson).- 1. Extremal sequences for some weighted zero-sum constants for cyclic groups (S.D. Adhikari, M.I. Molla, S. Paul).- 2. On a zero-sum problem arising from factorization theory (A. Bashir, A. Geroldinger, Q. Zhong).- 3. Conditional bounds on Siegel zeros (G. Bhowmik, K. Halupczok).- 4. Infinite co-minimal pairs in the integers and integral lattices (A. Biswas, J.P. Saha).- 5. Rigidity, graphs, and Hausdorff dimension (N. Chatzikonstantinou, A. Iosevich, S. Mkrtchyan, J. Pakianathan).- 6. On generalized harmonic numbers (Y.-G. Chen, B.-L. Wu).- 7. Partitions for semi-magic squares of size three (R. Donley).- 8. A sum of negative degrees of the gaps values in two-generated numerical semigroups and identities for the Hurwitz zeta function (L.G. Fel, T. Komatsu, A.I. Suriajaya).- 9. Widely digitally stable numbers (M. Filaseta, J. Juillerat, J. Southwick).- 10. Non-injectivity of nonzero discriminant polynomials and applications to packing polynomials (K. Gjaldbæk).- 11. Representing sequence subsums as sumsets of near equal sized sets (D.J. Grynkiewicz).- 12. Bounds on point configurations determined by distances and dot products (S. Gunter, E. Palsson, B. Rhodes, and S. Senger).- 13. Distribution of missing digits in diffsets (S. Harvey-Arnold, S.J. Miller, F. Peng).- 14. Recent progress in Hilbert cubes theory (N. Hegyvarı).- 15. Intrinsic characterization of representation functions and generalizations (C. Helou).- 16. Combinatorics of multicompositions (B. Hopkins, S. Ouvrey).- 17. A variant of the Elliott-Halberstam conjecture and the Goldbach conjecture (J.-J. Huang, H. Li).- 18. Part-frequency matrices, II: Recent work (W. Keith).- 19. A conjectural inequality for visible points in lattice parallelograms (G. Khan, M.R. Khan, J. Saha, P. Zhao).- 20. On a two-dimensional exponential sum (A. Kumchev).- 21. On consecutive perfect powers withelementary methods (P. Leonetti).- 22. Sidon sets and perturbations (M.B. Nathanson).- 23. Multiplicative representations and Ramsey’s Theorem (M.B. Nathanson).- 24. On distinct consecutive differences (I. Ruzsa, G. Shakan, J. Solymosi, E. Szemeredi).- 25. Limit points of Nathanson’s lambda sequences (S. Singh).