arXiv subjects

Thu Ha Trieu

Publications and source records attributed to Thu Ha Trieu.

2 recordsLinked to original sources

arXiv2025

The Mahler measure of exact polynomials and special $L$-values of $K3$ surfaces

We express the Mahler measure of an exact polynomial in arbitrarily many variables in terms of Deligne-Beilinson cohomology. We then focus on the relationship between the Mahler measure of four-variable exact polynomials and the special value of the $L$-function of $K3$ surfaces at $s = 4$. This result extends the three-variable case studied in \cite{Tri23}. Finally, we prove, under Beilinson's conjecture, that the Mahler measure of the polynomial $(x+1)(y+1)(z+1) + t$ is expressed in terms of the Riemann zeta function and the $L$-function of the modular form of weight 3 and level 7.

math.NT↗

arXiv2025

The Mahler measure of exact polynomials in three variables

We prove that under certain explicit conditions, the Mahler measure of a three-variable polynomial can be expressed in terms of elliptic curve $L$-values and Bloch-Wigner dilogarithmmic values, conditionally on Beilinson's conjecture. In some cases, these dilogarithmic values simplify to Dirichlet $L$-values. The proof involves a construction of an element in $K_4^{(3)}$ of a smooth projective curve over a number field. This generalizes a result of Lalín for the polynomial $z + (x+1)(y+1)$. We apply our method to several other Mahler measure identities conjectured by Boyd and Brunault.

math.NT↗