We study the densities of uniform random walks in the plane. A special focus is on the case
of short walks with three or four steps and, less completely, those with five steps. As one of …

The main goal of this survey is to give common characteristics of auxiliary hypergeometric
functions (and their generalisations), functions which occur in number-theoretic problems …

The Mahler measure of a polynomial in several variables has been a subject of much study
over the past thirty years—very few closed forms are proven but more are conjectured. In the …

We prove that sparse resultants having Mahler measure equal to zero are those whose
Newton polytope has dimension one. We then compute the Mahler measure of resultants in …

We consider the Mahler measure of the polynomial 1+ x 1+ x 2+ x 3+ x 4, which is the first
case not yet evaluated explicitly. A conjecture due to F. Rodriguez-Villegas represents this …

In Cogdell et al., LMS Lecture Notes Series 459, 393–427 (2020), the authors proved an
analogue of Kronecker's limit formula associated to any divisor $\mathcal D $ which is …

We calculate the second order derivatives of the Ronkin function in the case of an affine
linear polynomial in three variables and give an expression of them in terms of complete …

We prove formulas for special values of the Ramanujan tau zeta function. Our formulas show
that L (Δ, k) is a period in the sense of Kontsevich and Zagier when k⩾ 12. As an illustration …

arXiv:0803.0413v1 [math.NT] 4 Mar 2008 Page 1 arXiv:0803.0413v1 [math.NT] 4 Mar 2008
THE MAHLER MEASURE AND THE L-SERIES OF A SINGULAR K3 SURFACE MARIE JOSÉ …

Consider an algebraic number a. By definition, it is the zero in some field of an irreducible
polynomial Pa with integer coefficients. The complete set of zeros of such a polynomial …