PhD Defense Riccardo Pengo

PhD Defense Riccardo Pengo.

Title: "Mahler measures, special values of L-functions and complex multiplication"

Abstract: We will start by recalling what L-functions are, and explaining how their values at the integers are of arithmetic significance, following the conjectures of Beilinson and Bloch-Kato, as well as joint work in progress with Fabien Pazuki, which studies how these values measure the complexity of the objects they are attached to. We will then briefly review Mahler measures of polynomials, and give a roundup of types of identities relating special values of L-functions and Mahler measures, basing ourselves also on joint work in progress with François Brunault, concerning a certain exactness property of polynomials. We will finally summarize the main points of the theory of complex multiplication (CM), and sketch the proof of the main results of our PhD thesis, which concern the entanglement in the division fields of CM elliptic curves (jointly with Francesco Campagna) and the relations between the special value at the origin of the L-function associated to a CM elliptic curve E defined over the rationals, and the Mahler measure of some planar models of E.

 The majority of this talk will be aimed at a general mathematical audience, and a good part of it will also be understandable to an audience with little background in mathematics, but a sufficient amount of patience and curiosity.

Advisors: Ian Kiming, Fabien Pazuki


Assessment committee:

José Ignacio Burgos Gil (Instituto de Ciencias Matemáticas (ICMAT))

Morten Risager (University of Copenhagen), chair

Wadim Zudilin (Radboud Universiteit)


The defense will take place in Aud 1, AKB, for a limited number of participants, and for all the others via Zoom:

Email Ian Kiming ( for the meeting password.  

You can find a PDF copy of the thesis here: