[1]
J.R. Chen, “On the representation of a larger even integer as the sum of a prime and the product of at most two primes”, Scientia Sinica 16 (1973), 157–176.
References Bibliography
[2]
G. Cornell, J.H. Silverman, and G. Stevens, Modular forms and Fermat's last theorem, Springer (2000).
[3]
H. Davenport, Multiplicative number theory, third edition, Graduate Texts in Mathematics 74, Springer-Verlag, New York (2000).
[4]
L.E. Dickson, “A new extension of Dirichlet's therem on prime numbers”, Messenger of Mathematics 33 (1904), 155–161.
[5]
J. Friedlander and H. Iwaniec, Opera de Cribro, Colloquium Publications 57, American Mathematical Society, Providence (2010).
[6]
P.X. Gallagher, “On the distribution of primes in short intervals”, Mathematika 23 (1976), 4–9; corrigendum, ibid. 28 (1981), 86.
[7]
D.M. Goldfeld, “The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer”, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 4e série 3 (1976), 623–663.
[8]
D.A. Goldston, Y. Motohashi, J. Pintz, and C. Yıldırım, “Small gaps between primes exist”, Proc. Japan. Acad. 82 (2006), 61–65.
[9]
D.A. Goldston, J. Pintz, and C. Yıldırım, “Primes in tuples, I”, Annals of Mathematics 170 (2009), 819–862.
[10]
D.A. Goldston, J. Pintz, and C. Yıldırım, “Small gaps between primes”, Proceedings of the International Congress of Mathematicians–Seoul 2014 Vol. II, Kyung Moon Sa, Seoul (2014).
[11]
G.H. Hardy and J.E. Littlewood, “Some problems of `partitio numerorum.' III. On the expression of a number as a sum of primes”, Acta Mathematica 44 (1923), 1–70.
[12]
G.H. Hardy and E.M. Wright, An introduction to the theory of numbers, sixth edition, revised by D. R. Heath-Brown and J. H. Silverman, with a foreword by Andrew Wiles, Oxford University Press, Oxford (2008).
[13]
H. Iwaniec and E. Kowalski, Analytic number theory, Colloquium Publications 53, American Mathematical Society, Providence (2004).
[14]
G.J. Janusz, Algebraic number fields, second edition, Graduate Texts in Mathematics 7, American Mathematical Society (1996).
[15]
H.W. Lenstra, Jr. and P. Stevenhagen, “Chebotarëv and his density theorem”, http://www.math.leidenuniv.nl/~hwl/papers/cheb.pdf 1 .
[16]
J. Maynard, “Small gaps between primes”, Annals of Mathematics 181 (2015), 383–413.
[17]
Y. Motohashi and J. Pintz, “A smoothed GPY sieve”, Bulletin of the London Mathematical Society 40 (2008), 298–310.
[18]
M.R. Murty and S. Saradha, “On the Sieve of Eratosthenes”, Canadian Journal of Mathematics 39 (1987), 1107–1122.
[19]
M.B. Nathanson, Elementary methods in number theory, Graduate Texts in Mathematics 195, Springer-Verlag, New York (2000).
[20]
D. Platt and T. Trudgian, “The Riemann hypothesis is true up to \(3\cdot 10^{12}\)”, Bulletin of the London Mathematical Society 53 (2021), 792–797.
[21]
D.H.J. Polymath, “Variants of the Selberg sieve, and bounded intervals containing many primes”, Research in the Mathematical Sciences 1 (2014), article number 12.
[22]
A. Selberg, “An elementary proof of the prime number theorem”, Annals of Mathematics 50 (1949), 305–313.
[23]
J.-P. Serre, Abelian \(l\)-adic representations and elliptic curves, Research Notes in Mathematics 7, CRC Press (1998).
[24]
J.H Silverman, The arithmetic of elliptic curves, 2nd edition, Graduate Texts in Mathematics 106, Springer (2000).
[25]
K. Soundararajan, “Small gaps between prime numbers: the work of Goldston–Pintz–Yıldırım”, Bulletin of the American Mathematical Society 44 (2007), 1–18.
[26]
M. Watkins, “Class number one from analytic rank two”, Mathematika 65 (2019), 333–374.
[27]
M. Watkins, “Class numbers of imaginary quadratic fields”, Mathematics of Computation 73 (2003), 907–938.
[28]
D. Zagier, “Newman's short proof of the Prime Number Theorem”, American Mathematical Monthly 104 (1997), 705–708.
[29]
Y. Zhang, “Bouned gaps between primes”, Annals of Mathematics 179 (2014), 1121–1174.
