Andrew V. Sutherland

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math.NT2020

Computing L-Polynomials of Picard curves from Cartier-Manin matrices

Sualeh Asif, Francesc Fité, Dylan Pentland

We study the sequence of zeta functions $Z (C_{p}, T)$ of a generic Picard curve $C : y^{3} = f (x)$ defined over $Q$ at primes $p$ of good reduction for $C$ . We define a degree 9 po…

math.NT2020

On a question of Mordell

Andrew R. Booker, Andrew V. Sutherland

We make several improvements to methods for finding integer solutions to $x^{3} + y^{3} + z^{3} = k$ for small values of $k$ . We implemented these improvements on Charity Engine's global compu…

math.NT2020

Sorting and labelling integral ideals in a number field

John Cremona, Aurel Page, Andrew V. Sutherland

We define a scheme for labelling and ordering integral ideals of number fields, including prime ideals as a special case. The order we define depends only on the choice of a monic…

math.NT2019

Arithmetic invariants from Sato--Tate moments

Edgar Costa, Francesc Fité, Andrew V. Sutherland

We give some arithmetic-geometric interpretations of the moments M_2[a_1], M_1[a_2], and M_1[s_2] of the Sato-Tate group of an abelian variety A defined over a number field by rela…