# Publications

**Book:**

Discrete Mathematics (German) - Springer-Spektrum (2019)

**Peer-reviewed articles:**

[1] Two remarks on Narkiewicz's property (P) - accepted for publication in *Res. Number Theory* 8, 60 (2022) [open access]

[2] Wandering points for the Mahler measure (with P. Fili and M. Zhang) - *Acta Arith.* 204 (2022), no.3, pp.225-252 [arXiv]

[3] Perfect powers in value sets and orbits of polynomials (with A. Ostafe and I. Shparlinski) - *New York J. Math. 27 *(2021), pp.903-917 [open access]

[4] Fields generated by finite rank subgroups of \(\overline{\mathbb{Q}}^*\) - *Int. J. Number Theory* 17 (2021), no.5, pp.1079-1089 [arXiv]

[5] On the behavior of Mahler's measure under iteration (with P. Fili and M. Zhang) - *Monatsh. Math*. 193 (2020), no.1, pp.61-86 [open access]

[6] Quantitative height bounds under splitting conditions (with P. Fili) - *Trans. Amer. Math. Soc.* 372 (2019), no.7, pp.4605-4626 [arXiv]

[7] Small totally *p*-adic algebraic numbers - *Int. J. Number Theory *14 (2018), no.10, pp.2687-2697 [arXiv]

*The content of *[7] *is also covered in the nice book Around the unit circle, by J. McKee and C. Smyth.*

[8] A note on extensions of \(\mathbb{Q}^{\rm tr}\) - J. Théor. Nombres Bordeaux 28 (2016), no.3, pp.735-742 [arXiv]

[9] Heights and totally *p*-adic numbers - *Acta Arith.* 171 (2015), no.3, pp.277-291 [arXiv, video]

[10] Small points and free abelian groups (with R. Grizzard and P. Habegger) - Int. Math. Res. Not. (2015), no.20, pp.10657-10679 [arXiv]

[11] Heights of points with bounded ramification - Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 14 (2015), no.3, pp.965-981 [arXiv]

[12] Heights and totally real numbers - *Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.* 24 (2013), no.4, pp.471-483 [arXiv]

**Theses:**

Fields with the Bogomolov property [pdf] (PhD-thesis, advisor: W. Gubler)

Density of squarefree values of integer polynomials [pdf] (Diploma-thesis, German)

**Miscellaneous:**

News on quadratic polynomials - Snapshots on Modern Mathematics from Oberwolfach no.2 (2017) [pdf]

Height bounds for algebraic numbers under splitting conditions (with P. Fili) - Oberwolfach Reports no.21 (2016) [pdf]

A dynamical Bogomolov property - unpublished note (2011) [arXiv]