[See also Combinatorial number theory.]
--------------------------------------------------
20082 Martin Aigner/Volker Schulze: Mr. Summe und Mr. Produkt.
Math. Sember. 55 (2008), 7-17.

24676 Mathias Beiglböck: Arithmetical progressions in abundance by
combinatorial tools. Proc. AMS ..., 2p.

17688 Mathias Beiglböck/Vitaly Bergelson/Neil Hindman/Dona Strauss: Some new results
in multiplicative and additive Ramsey theory.
Trans. AMS 360/2 (2008), 819-847.

23321 Mathias Beiglböck/Reinhard Winkler: Endre Szemeredi - ein mathematisches
Universum in kombinatorischem Gewande. IMN 221 (2012), 21-38.

26818 Michael Bennett/Vandita Patel/Samir Siksek: Perfect powers that are sums of
consecutive cubes. Arxiv 2016, 18p.

22910 Wolfgang Blum: Goldbach und die Zwillinge.
Spektrum Dezember 2008, 94-99.

24594 Tom Brown/Peter Jau-Shyong Shiue: On the history of van der Waerden's
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24329 R. Buck: The measure theoretic approach to density.
Am. J. Math. 68/4 (1946), 560-580.

22913 J. Deshouillers/G. Effinger/H. te Riele/D. Zinoviev:] A complete Vinogradov
3-primes theorem under the Riemann hypothesis.
Electron. Res. Announce AMS 3 (1997), 99-104.

22911 Jean-Marc Deshouillers/Andrew Granville/Wladyslaw Narkiewicz/Carl Pomerance:
An upper bound in Goldbach's problem. Math. Comp. 61/203 (1993), 209-213.

Harold Diamond/H.Halberstam: Differential difference equations in analytic 
number theory. See Zentralblatt 760 (1993), 44.

A. Fraenkel: Systems of numeration. Am. Math. Monthly 92 (1985), 105-114.

A. Fraenkel: The use and usefulness of numeration systems.
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21089 Michael Freeze/Weidong Gao/Alfred Geroldinger: The critical number
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C. Frougny: Representations of numbers and finite automata.
Math. Syst. Theory 25 (1992), 37-60.

C. Frougny: Linear numeration systems of order two.
Inf. and Comp. 77 (1988), 233-259.

C. Frougny: Systemes de numeration lineaires et theta-representations.
Theor. Comp. Sci. 94 (1992), 223-236.

C. Frougny/B. Solomyak: Finite beta-expansions.
Erg. Th. and Dyn. Syst. 12 (1992), 713-723.

Hillel Furstenberg/Y. Katznelson/D. Ornstein: The ergodic theoretical
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27365 Solomon Golomb: Arithmetica topologica.
In Gen. Top. Rel. Mod. An. Algebra 1961, 179-186.
[Furstenbergs topology on the integers.]

Timothy Gowers: A new proof of Szemeredi's theorem.
Geom. Funct. Anal. 11 (2001), 465-588.

27011 Timothy Gowers: Generalizations of Fourier analysis, and how to apply them.
Bull. AMS ... (2016), 44p.

27228 Ronald Graham/B. Rothschild: A short proof on van der Waerden's theorem
on arithmetic progressions. Proc. AMS 42/2 (1974), 385-386.

25280 Andrew Granville/Friedrich Roesler: The set of differences of a given set. Internet, 8p.

Andrew Granville: Integers, without large prime factors, in arithmetic 
progressions I. Acta Math. 170 (1993), 255-273.

22912 Andrew Granville: Refinements of Goldbach's conjecture, and the
generalized Riemann hypothesis. Funct. Approx. 37 (2007), 7-21.

24139 Ben Green: Review of the book "Additive combinatorics" by Tao/Vu.
Bull. AMS 46/3 (2009), 489-497.

24640 Matthew Guay: Topological dynamics and van der Waerden's theorem.
Internet 2009, 10p.

1932 H. Halberstam/K. Roth: Sequences. Springer 1983.

Hamidoune/G. Zemor: On zero-free subset sums. Acta Arithm. 78 (1996), 143-152.

25342 Godfrey Hardy/John Littlewood: Some problems of partitio numerorum III:
on the expression of a number as a sum of primes. Acta Math. 44 (1923), 1-70.

David Hayes/G. Effinger: Additive number theory of polynomials over a
finite field. Oxford UP 1991.

23734 Harald Helfgott: Major arcs for Goldbach's problem. Internet 2013, 133p.
Possibly a proof of the weak Goldbach conjecture (every odd integer > 5 is
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1892 C.Hooley: On Waring's problem. Acta Math. 157 (1986), 49-97. [3323]

28332 Patrick Honner: Why the sum of three cubes is a hard math problem.
Quanta 5 November 2019, 3p. A new representation of 3 as a sum
of three cubes.

1899 Loo-Keng Hua: Abschaetzungen von Exponentialsummen und ihre Anwendung in 
der Zahlentheorie. Enz. math. Wiss. 12/Heft 13,1.

1880 Loo-Keng Hua: Additive Primzahltheorie. Leipzig 1959.

23320 Mihyun Kang: The 2012 Abel laureate Endre Szemeredi and his
celebrated work. IMN 221 (2012), 1-19.

29049 Aubrey Kempner: The development of "Partitio numerorum", with particular reference to
the work of messrs. Hardy, Littlewood and Ramanujan. Part I.
Am. Math. Monthly 30/7 (1923), 354-369.

29050 Aubrey Kempner: The development of "Partitio numerorum", with particular reference to
the work of messrs. Hardy, Littlewood and Ramanujan. Part II.
Am. Math. Monthly 30/7 (1923), 416-425.

22557 A. Kumchev/D. Tolev: An invitation to additive prime number theory.
Serdica Math. J. 31 (2005), 1-74.

6681 Edmund Landau: Ueber einige neuere Fortschritte der additiven 
Zahlentheorie. Stechert-Hafner 1964.

27096 Alessandro Languasco: La congettura di Goldbach.
Tesi Dott. Univ. Torino 1995, 100p.

22211 Alessandro Languasco/Alessandro Zaccagnini: The number of
Goldbach representations of an integer.
Proc. AMS ... (2011), 10p.

23735 Alessandro Languasco/Alessandro Zaccagnini: A Cesaro average of Goldbach
numbers. Internet 2012, 12p.

10817 Dana Mackenzie: Fractions to make an Egyptian scribe blanch.
Science 10 October 1997, 224.

25149 Preda Mihailescu: On some conjectures in additive number theory.
EMS Newsletter June 2014, 13-16.

22413 Melvyn Nathanson: Additive number theory - the classical bases.
Springer 2010, 350p. Eur 63.
" ... eine sehr gute Darstellung ... Das vorliegende Werk ist angenehm
zu lesen und kann bestens als Grundlage fu''r eine Spezialvorlesung
empfohlen werden." (Robert Tichy)

Melvyn Nathanson: Additive number theory. Inverse theorems and the
geometry of sumsets. Springer 1996, 350p. 3-540-94655-1. DM 78.

2074 Hans-Heinrich Ostmann: Additive Zahlentheorie. 2 volumes. Springer 1968.

24332 Milan Pasteka: Some properties of Buck's measure density.
Math. Slovaca 42/1 (1992), 15-32.

28333 Sarah Peluse: Bounds for sets with no polynomial progressions.
Arxiv 1909.00309 (2019), 52p.

23088 Georg Johann Rieger: Ãœber die Folge der Zahlen der Gestalt p1+p2.
Arch. Math. 15 (1964), 33-41.

1963 P. Ross: On Chen's theorem that each large even number has the form
p1+p2 or p1+p2p3. J. London Math. Soc. 10 (1975), 500-506. [3323]

25670 N. Saradha/R. Thangadurai: Pillai's problem on consecutive integers.
Number theory appl. ... (2009), 175-188.

26938 Christoph Scriba: Zur Entwicklung der additiven Zahlentheorie von Fermat
bis Jacobi. Jber. DMV 72 (1970), 122-142.

25283 Tarlok Shorey/R. Tijdeman: Prime factors of arithmetic progressions and binomial coefficients.
In U. Zannier (ed.): Diophantine geometry. SNS Pisa 2007, 283-296.

5761 Matti Sinisalo: Checking the Goldbach conjecture up to 4*10^11.
Math. Comp. 61 (1993), 931-934.

E. Szemeredi: On sets of integers containing no four elements in
arithmetic progression. Acta Math. Acad. Sci. Hung. 20 (1969), 89-104.

22972 Terence Tao: The dichotomy between structure and randomness, arithmetic
progressions, and the primes. Internet 2005, 27p.

24038 Terence Tao: [Lectures on additive combinatorics.] Internet ca. 2006, 118p.

24182 Terence Tao/Van Vu: Additive combinatorics. Cambridge UP 2010, 510p. Eur 38.

R. Vaughan: On the representation of numbers as sums of powers of natural
numbers. Proc. LMS 21 (1970), 160-180.

R. Vaughan: On sums of mixed powers. J. LMS 3 (1971), 677-688.

R. Vaughan: On the addition of sequences of integers.
J. Number Theory 4 (1972), 1-16.

R. Vaughan: On Goldbach's problem. Acta Arithm. 22 (1972), 21-48.

R. Vaughan: A note on Schnirelman's approach to Goldbach's problem.
Bull. LMS 8 (1976), 245-250.

R. Vaughan: Homogeneous additive equations and Waring's problem.
Acta Arithm. 33 (1977), 231-253.

R. Vaughan: A survey of some important problems in additive number theory.
Asterisque 61 (1979), 213-222.

R. Vaughan: Recent work in additive prime number theory.
Proc. ICM Helsinki 1978, 389-394.

R. Vaughan: A ternary additive problem.
Proc. LMS 41 (1980), 516-532.

R. Vaughan: Sums of three cubes. Bull. LMS 17 (1985), 17-20.

R. Vaughan: On Waring's problem for smaller exponents I-II.
Proc. LMS 52 (1986), 445-463, Mathematika 33 (1986), 6-22.

R. Vaughan: On Waring's problem for sixth powers.
J. LMS 33 (1986), 227-236.

R. Vaughan: On Waring's problem for cubes I-II.
J. reine u. angew. Math. 365 (1986), 122-170, J. LMS 39 (1989), 205-218.

R. Vaughan: On Waring's problem. One square and five cubes.
Quart. J. Math. 37 (1986), 117-127.

R. Vaughan: A new iterative method in Waring's problem I-II.
Acta Arithm. 162 (1989), 1-71, J. LMS 39 (1989), 219-230.

R. Vaughan: The Hardy-Littlewood method. Cambridge UP 1997, 230p. Pds. 35.

R. Vaughan/H. Montgomery: Error terms in additive prime number theory.
Oxford Quarterly J. 24 (1973), 207-216.

R. Vaughan/H. Montgomery: The exceptional set in Goldbach's problem.
Acta Arithm. 27 (1975), 353-370.

R. Vaughan/Hans Riesel: On sums of primes. Arkif f. Mat. 21 (1983), 45-74.

R. Vaughan/T. Wooley: On Waring's problem Some refinements.
Proc. LMS 63 (1991), 35-68.

R. Vaughan/T. Wooley: Further improvements in Waring's problem
I - II (Sixth powers) - III (Eighth powers).
Acta Math., ca. 1994, Duke Math. J. 76 (1994), 683-710,
Phil. Trans. Royal Soc. London A 345 (1993), 385-396.

3612 Yuan Wang: Diophantine equations and inequalities in algebraic number
fields. Springer 1991.

3261 Yuan Wang (ed.): Goldbach conjecture. World Scientific 1984.

Alessandro Zaccagnini: On the exceptional set for the sum of a prime and a 
k-th power. Mathematika 39 (1992), 400-421. On the Hardy/Littlewood conjecture.