Publications and preprints

M. Crabit Nicolau
Generating series techniques for computing Darmon-Dasgupta units over real quadratic fields  (pdf, code)
(To appear in ANTS XVII proceedings)
We give a new efficient algorithm to compute p-units that live in abelian extensions of real quadratic fields. This algorithm builds on recent work of Charollois which provides formulas for the p-adic interpolation of special values of Lerch's cotangent zeta function. These special values, which we us to calculate these p-units, are given as coefficients of product of elementary generating series. The bottleneck of these computations is to compute quickly these coefficients.

M. Crabit Nicolau
An archimedean approach to Singular Moduli on Shimura curves  (arxiv)
(submitted)
We give a new proof of a result of Daas. This result is a generalization to Shimura curve of genus 0 of the work of Gross and Zagier in On singular moduli. Our approach, based on evaluating Green’s functions on the Shimura curve at CM points, closely follows the structure of the original analytic proof. We try to give some insight on the similarities between the p-adic proof of Daas and our archimedean proof.