[1]
Assani, I., Duncan, D. and Moore, R.. Pointwise characteristic factors for Wiener–Wintner double recurrence theorem. Ergod. Th. & Dynam. Sys. to appear. *Preprint*, 2014, arXiv:1402.7094.
[2]
Assani, I. and Moore, R.. Extension of Wiener–Wintner double recurrence theorem to polynomials. J. Anal. Math. to appear. *Preprint*, 2014, arXiv:1409.0463.
[3]
Assani, I. and Moore, R.. A good universal weight for nonconventional ergodic averages in norm. Ergod. Th. & Dynam. Sys. to appear. *Preprint*, 2015, arXiv:1503.08863.
[4]
Assani, I. and Moore, R.. A good universal weight for multiple recurrence averages with commuting transformations in norm. *Preprint*, 2015, arXiv:1506.06730.
[5]
Auslander, J.. Minimal Flows and Their Extensions. North-Holland, Amsterdam, 1988.

[6]
Auslander, L., Green, L. and Hahn, F.. Flows on homogeneous spaces. With the assistance of L. Markus and W. Massey, and an appendix by L. Greenberg.
*(Annals of Mathematics Studies, 53)*
. Princeton University Press, Princeton, NJ, 1963.

[7]
Austin, T.. On the norm convergence of nonconventional ergodic averages. Ergod. Th. & Dynam. Sys.
30 (2010), 321–338.

[8]
Austin, T.. Pleasant extensions retaining algebraic structure, I. J. Anal. Math.
125 (2015), 1–36.

[9]
Austin, T.. Pleasant extensions retaining algebraic structure, II. J. Anal. Math.
126 (2015), 1–111.

[10]
Bergelson, V.. Weakly mixing PET. Ergod. Th. & Dynam. Sys.
7(3) (1987), 337–349.

[11]
Bergelson, V., Host, B. and Kra, B.. Multiple recurrence and nilsequences. Invent. Math.
160(2) (2005), 261–303, With an appendix by I. Ruzsa.

[12]
Bergelson, V. and Leibman, A.. Polynomial extensions of van der Waerden’s and Szemerédi’s theorems. J. Amer. Math. Soc.
9 (1996), 725–753.

[13]
Bergelson, V. and McCutcheon, R.. An ergodic IP polynomial Szemerédi theorem. Mem. Amer. Math. Soc.
146 (2000), 695.

[14]
Boshernitzan, M.. An extension of Hardy’s class L of ‘Orders of Infinity’. J. Anal. Math.
39 (1981), 235–255.

[15]
Boshernitzan, M.. Uniform distribution and Hardy fields. J. Anal. Math.
62 (1994), 225–240.

[16]
Boshernitzan, M., Kolesnik, G., Quas, A. and Wierdl, M.. Ergodic averaging sequences. J. Anal. Math.
95 (2005), 63–103.

[17]
Camarena, A. and Szegedy, B.. Nilspaces, nilmanifolds and their morphisms. *Preprint*, 2012, arXiv:1009.3825v3.
[18]
Chu, Q.. Convergence of weighted polynomial multiple ergodic averages. Proc. Amer. Math. Soc.
137(4) (2009), 1363–1369.

[19]
Chu, Q., Frantzikinakis, N. and Host, B.. Commuting averages with polynomial iterates of distinct degrees. Proc. Lond. Math. Soc. (3)
102(5) (2011), 801–842.

[20]
Conze, J.-P. and Lesigne, E.. Théorèmes ergodiques pour des mesures diagonales. Bull. Soc. Math. France
112(2) (1984), 143–175.

[21]
Conze, J.-P. and Lesigne, E.. Sur un théorème ergodique pour des mesures diagonales. Probabilités, Publ. Inst. Rech. Math. Rennes, 1987-1. Université Rennes I, Rennes, 1988, pp. 1–31.

[22]
Daboussi, H.. Fonctions multiplicatives presque périodiques B. D’après un travail commun avec Hubert Delange. Journées Arithmétiques de Bordeaux (Conference, Université Bordeaux, Bordeaux, 1974)
*(Astérisque, 24–25)*
. Société Mathématique de France, Paris, 1975, pp. 321–324.

[23]
Daboussi, H. and Delange, H.. Quelques proprietes des functions multiplicatives de module au plus egal 1. C. R. Acad. Sci. Paris Ser. A
278 (1974), 657–660.

[24]
Daboussi, H. and Delange, H.. On multiplicative arithmetical functions whose modulus does not exceed one. J. Lond. Math. Soc. (2)
26(2) (1982), 245–264.

[25]
Eisner, T.. Linear sequences and weighted ergodic theorems. Abstr. Appl. Anal. (2013), Art. ID 815726.

[26]
Eisner, T. and Krause, B.. (Uniform) convergence of twisted ergodic averages. Ergod. Th. & Dynam. Sys. to appear. *Preprint*, 2014, arXiv:1407.4736.
[27]
Elliott, P.. Probabilistic Number Theory I. Springer, New York, 1979.

[28]
Frantzikinakis, N.. Equidistribution of sparse sequences on nilmanifolds. J. Anal. Math.
109 (2009), 353–395.

[29]
Frantzikinakis, N.. Multiple correlation sequences and nilsequences. Invent. Math.
202(2) (2015), 875–892.

[30]
Frantzikinakis, N. and Host, B.. Higher order Fourier analysis of multiplicative functions and applications. J. Amer. Math. Soc. to appear. *Preprint*, 2014, arXiv:1403.0945.
[31]
Frantzikinakis, N. and Host, B.. Multiple ergodic theorems for arithmetic sets. Trans. Amer. Math. Soc. to appear. *Preprint*, 2015, arXiv:1503.07154.
[32]
Frantzikinakis, N., Host, B. and Kra, B.. The multidimensional Szemerédi theorem along shifted primes. Israel J. Math.
194(1) (2013), 331–348.

[33]
Furstenberg, H.. Recurrence in ergodic theory and combinatorial number theory. Princeton University Press, Princeton, NJ, 1981.

[34]
Furstenberg, H. and Weiss, B.. A mean ergodic theorem for (1/*N*)∑_{
n=1}
^{
N
}
*f* (*T*
^{
n
}
*x*)*g* (*T*
^{
n
2
}
*x*). Convergence in ergodic theory and probability (Columbus, OH, 1993)
*(Ohio State University Mathematical Research Institute Publications, 5)*
. de Gruyter, Berlin, 1996, pp. 193–227.

[35]
Glasner, E.. Ergodic Theory via Joinings
*(Mathematical Surveys Monographs, vol. 101)*
. American Mathematical Society, Providence, RI, 2003.

[36]
Granville, A. and Soundararajan, K.. *Multiplicative Number Theory: The Pretentious Approach*. Book manuscript in preparation.

[37]
Green, B. and Tao, T.. An inverse theorem for the Gowers *U*
^{3}(*G*)-norm. Proc. Edinb. Math. Soc.
51(1) (2008), 73–153.

[38]
Green, B. and Tao, T.. The quantitative behaviour of polynomial orbits on nilmanifolds. Ann. of Math. (2)
175(2) (2012), 465–540.

[39]
Green, B. and Tao, T.. On the quantitative distribution of polynomial nilsequences-erratum. Ann. of Math. (2)
179(3) (2014), 1175–1183. arXiv:1311.6170v3.
[40]
Green, B., Tao, T. and Ziegler, T.. An inverse theorem for the Gowers *U*
^{
s+1}[*N*]-norm. Ann. of Math. (2)
176(2) (2012), 1231–1372.

[42]
Halász, G.. Über die Mittelwerte multiplikativer zahlentheoretischer Funktionen. Acta Math. Acad. Sci. Hung.
19 (1968), 365–403.

[43]
Host, B.. Ergodic seminorms for commuting transformations and applications. Studia Math.
195 (2009), 31–49.

[44]
Host, B. and Kra, B.. Nonconventional ergodic averages and nilmanifolds. Ann. of Math. (2)
161 (2005), 397–488.

[45]
Host, B. and Kra, B.. Convergence of polynomial ergodic averages. Israel J. Math.
149 (2005), 1–19.

[46]
Host, B. and Kra, B.. Uniformity seminorms on *ℓ*
^{
∞
} and applications. J. Anal. Math.
108 (2009), 219–276.

[47]
Host, B. and Kra, B.. A point of view on Gowers uniformity norms. New York J. Math.
18 (2012), 213–248.

[48]
Kátai, I.. A remark on a theorem of H. Daboussi. Acta Math. Hungar.
47 (1986), 223–225.

[49]
Kechris, A.. Classical descriptive set theory
*(Graduate Texts in Mathematics, 156)*
. Springer, New York, 1995.

[50]
Leibman, A.. Pointwise convergence of ergodic averages for polynomial sequences of translations on a nilmanifold. Ergod. Th. & Dynam. Sys.
25(1) (2005), 201–213.

[51]
Leibman, A.. Pointwise convergence of ergodic averages for polynomial actions of ℤ^{
d
} by translations on a nilmanifold. Ergod. Th. & Dynam. Sys.
25(1) (2005), 215–225.

[52]
Leibman, A.. Convergence of multiple ergodic averages along polynomials of several variables. Israel J. Math.
146 (2005), 303–316.

[53]
Leibman, A.. Multiple polynomial correlation sequences and nilsequences. Ergod. Th. & Dynam. Sys.
30(3) (2010), 841–854.

[54]
Leibman, A.. Nilsequences, null-sequences, and multiple correlation sequences. Ergod. Th. & Dynam. Sys.
35(1) (2015), 176–191.

[55]
Leibman, A.. Correction to the paper ‘Nilsequences, null-sequences, and multiple correlation sequences’. *Preprint*, 2012, arXiv:1205.4004.
[56]
Lesigne., E.. Sur une nil-variété, les parties minimales associées à une translation sont uniquement ergodiques. Ergod. Th. & Dynam. Sys.
11(2) (1991), 379–391.

[58]
Parry, W.. Ergodic properties of affine transformations and flows on nilmanifolds. Amer. J. Math.
91 (1969), 757–771.

[59]
Parry, W.. Dynamical systems on nilmanifolds. Bull. Lond. Math. Soc.
2 (1970), 37–40.

[60]
Rudolph, D.. Eigenfunctions of *T* × *S* and the Conze–Lesigne algebra. Ergodic Theory and its Connections with Harmonic Analysis (Alexandria, 1993).
*(London Mathematical Society Lecture Note Series, 205)*
. Cambridge University Press, Cambridge, 1995, pp. 369–432.

[61]
Szegedy, B.. On higher order Fourier analysis. *Preprint*, 2012, arXiv:1203.2260v1.
[62]
Tao, T.. Norm convergence of multiple ergodic averages for commuting transformations. Ergod. Th. & Dynam. Sys.
28(2) (2008), 657–688.

[64]
Walsh, M.. Norm convergence of nilpotent ergodic averages. Ann. of Math. (2)
175(3) (2012), 1667–1688.

[65]
Wirsing, E.. Das asymptotische Verhalten von Summen uber multiplikative Funktionen, II. Acta Math. Acad. Sci. Hungar
18 (1967), 411–467.

[66]
Ziegler, T.. Universal characteristic factors and Furstenberg averages. J. Amer. Math. Soc.
20 (2007), 53–97.

[67]
Zorin-Kranich, P.. Norm convergence of multiple ergodic averages on amenable groups. J. Anal. Math. to appear. *Preprint*, 2011, arXiv:1111.7292.
[68]
Zorin-Kranich, P.. A uniform nilsequence Wiener–Wintner theorem for bilinear ergodic averages. *Preprint*, 2015, arXiv:1504.04647.