39 citations · 44 across the 8 of their papers we have counts for
8 papers
First order p-adic deformations of weight one newforms
Henri Darmon, Alan Lauder, Victor Rotger
This article studies the first-order -adic deformations of classical weight one newforms, relating their fourier coefficients to the -adic logarithms of algebraic numbers in…
A computation of modular forms of weight one and small level
Kevin Buzzard, Alan Lauder
We report on a computation of holomorphic cuspidal modular forms of weight one and small level (currently level at most ) and classification of them according to the projecti…
Efficient computation of Rankin p-adic L-functions
Alan G. B. Lauder
We present an efficient algorithm for computing certain special values of Rankin triple product -adic L-functions and give an application of this to the explicit construction of…
Degenerations and limit Frobenius structures in rigid cohomology
Alan G. B. Lauder
We introduce a "limiting Frobenius structure" attached to any degeneration of projective varieties over a finite field of characteristic p which satisfies a p-adic lifting assumpti…
Ranks of elliptic curves over function fields
Alan G. B. Lauder
We present experimental evidence to support the widely held belief that one half of all elliptic curves have infinitely many rational points. The method used to gather this evidenc…
Counting points on varieties over finite fields of small characteristic
Alan G. B. Lauder, Daqing Wan
We present a deterministic polynomial time algorithm for computing the zeta function of an arbitrary variety of fixed dimension over a finite field of small characteristic. One con…