Recent papers

Recent papers on Landau's problems on prime numbers, surfaced by the prominence of their authors in this directory.

Showing 15 papers, ranked by the Top 100 standing of their authors then by recency. Authors who appear in the Top 100 are shown in bold.

#	Title	Authors	Published	Best rank
1	Diophantine approximation with primes from short intervals	Stephan Baier, Sayantan Roy	2025-12	#10
2	The average number of representations of an integer as a sum of two prime powers over multiples of a fixed integer	Alessandra Migliaccio, Alessandro Zaccagnini	2026-03	#18
3	Theorem $(1+1.9)$ on the Goldbach Conjecture	Jiamin Li, Jianya Liu	2026-06	#28
4	Binomial coefficients with divisors avoiding an interval	Hung M. Bui, Kyle Pratt, Alexandru Zaharescu	2026-05	#47
5	An Explicit Result for the Sum of Two Almost Primes	Adrian Dudek, Lachlan Dunn	2026-02	#49
6	Representations of positive integers by three almost-prime squares	Yue-Feng She, Yu-Chen Sun, Guang-Liang Zhou	2026-06	#50
7	An update on the Linnik--Goldbach and Romanov problems	Daniel R. Johnston, Tim Trudgian	2026-05	#65
8	Short Exponential Sums and Ternary Correlations of Multiplicative Functions	Jiseong Kim	2026-03	#66
9	On binary correlations of Fourier coefficients of holomorphic cusp forms at prime arguments	Jiseong Kim, Kunjakanan Nath	2025-11	#66
10	On Averages of Shifted Convolutions with Applications to $GL(2)$ and $GL(3)$ Fourier Coefficients	Jiseong Kim	2025-09	#66
11	The trigonometric polynomial on sums of two squares, an additive problem and generalisation	Olivier Ramare, GK Viswanadham	2025-09	#74
12	A new class of Correlations insisting on Ramanujan expansions	Giovanni Coppola	2026-02	#76
13	Sierpinski's Hypothesis H1	Matt Visser	2025-12	#83
14	Surviving Eratosthenes sieve I: quadratic density and Legendre's conjecture	Fred B. Holt	2026-03	#89
15	The exceptional set for Diophantine inequality with mixed powers of primes	Yu Fu, Linzhu Fu, Liqun Hu	2026-04	#99

Most cited (all time)

The ten most-cited Mathematics works on Landau's problems on prime numbers, by citation count in OpenAlex. Results are filtered to the Mathematics field (OpenAlex field 26) and ranked by total citations.

The Top 100 ranking is designed to capture prominent, currently active researchers. If an author in this table is not linked to a profile, it is usually because they are deceased or less active than the researchers in the ranking, not because they are less significant to the field.

#	Title	Authors	Year	Citations
1	Bounded gaps between primes DOI	Zhang Yitang	2014	463
2	Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅10¹⁸ DOI	Tomás Oliveira e Silva; Siegfried Herzog; Silvio Pardi	2013	165
3	The ternary Goldbach conjecture is true DOI	H. A. Helfgott	2013	99
4	Verifying the Goldbach conjecture up to 4⋅10¹⁴ DOI	J. Richstein	2000	64
5	Irregularities in the distribution of primes and twin primes DOI	Richard P. Brent	1975	55
6	Average twin prime conjecture for elliptic curves DOI	Antal Balog; Alina-Carmen Cojocaru; Chantal David	2011	50
7	Evaluation of Artin’s constant and the twin-prime constant DOI	John W. Wrench	1961	48
8	Chen's double sieve, Goldbach's conjecture and the twin prime problem DOI	Jie Wu	2004	47
9	Bounded gaps between primes with a given primitive root DOI	Paul Pollack	2014	39
10	On the Vinogradov bound in the three primes Goldbach conjecture DOI	Mengmeng Liu; Tianze Wang	2002	36