5 citations · 8 across the 4 of their papers we have counts for
9 papers
Quadratic Chabauty for modular curves: Algorithms and examples
Jennifer S. Balakrishnan, Netan Dogra, Jan Steffen Müller +2
We describe how the quadratic Chabauty method may be applied to explicitly determine the set of rational points on modular curves of genus whose Jacobians have Mordell--Weil…
Explicit Chabauty-Kim for the Split Cartan Modular Curve of Level 13
Jennifer S. Balakrishnan, Netan Dogra, J. Steffen Müller +2
We extend the explicit quadratic Chabauty methods developed in previous work by the first two authors to the case of non-hyperelliptic curves. This results in an algorithm to compu…
Explicit Coleman integration for curves
Jennifer S. Balakrishnan, Jan Tuitman
The Coleman integral is a -adic line integral that plays a key role in computing several important invariants in arithmetic geometry. We give an algorithm for explicit Coleman i…
Computing zeta functions of generic projective hypersurfaces in larger characteristic
Jan Tuitman
We give improvements of the deformation method for computing the zeta function of a generic projective hypersurface in characteristic~ that either reduce the dependence on~ o…
Point counting on curves using a gonality preserving lift
Wouter Castryck, Jan Tuitman
We study the problem of lifting curves from finite fields to number fields in a genus and gonality preserving way. More precisely, we sketch how this can be done efficiently for cu…
Counting points on curves using a map to P^1, II
Jan Tuitman
We introduce a new algorithm to compute the zeta function of a curve over a finite field. This method extends previous work of ours to all curves for which a good lift to character…
Counting points on curves using a map to P^1
Jan Tuitman
We introduce a new algorithm to compute the zeta function of a curve over a finite field. This method extends Kedlaya's algorithm to a very general class of curves using a map to t…
Improvements to the deformation method for counting points on smooth projective hypersurfaces
Sebastian Pancratz, Jan Tuitman
We present various improvements to the deformation method for computing the zeta function of smooth projective hypersurfaces over finite fields using -adic cohomology. This incl…
Effective convergence bounds for Frobenius structures on connections
Kiran S. Kedlaya, Jan Tuitman
Consider a meromorphic connection on P^1 over a p-adic field. In many cases, such as those arising from Picard-Fuchs equations or Gauss-Manin connections, this connection admits a…