Vol. 2, 2019
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Proceedings of the Thirteenth Algorithmic Number Theory Symposium
Edited by Renate Scheidler and Jonathan Sorenson
DOI:
10.2140/obs.2019.2-1
Contents
Preface
vii–x
Renate Scheidler and Jonathan Sorenson
Counting points on genus-$3$ hyperelliptic curves with explicit real multiplication
1–19
Simon Abelard, Pierrick Gaudry and Pierre-Jean Spaenlehauer
Constructing Picard curves with complex multiplication using the Chinese remainder theorem
21–36
Sonny Arora and Kirsten Eisenträger
Computing zeta functions of cyclic covers in large characteristic
37–53
Vishal Arul, Alex J. Best, Edgar Costa, Richard Magner and Nicholas Triantafillou
Computing normalizers of tiled orders in $M_n(k)$
55–68
Angelica Babei
Computation of triangular integral bases
69–84
Jens-Dietrich Bauch and Ha Thanh Nguyen Tran
Explicit Coleman integration in larger characteristic
85–102
Alex J. Best
Fast multiquadratic $S$-unit computation and application to the calculation of class groups
103–118
Jean-François Biasse and Christine Van Vredendaal
Fast coefficient computation for algebraic power series in positive characteristic
119–135
Alin Bostan, Xavier Caruso, Gilles Christol and Philippe Dumas
Explicit computations in Iwasawa theory
137–153
Reinier Bröker, David Hubbard and Lawrence C. Washington
Numerical computation of endomorphism rings of Jacobians
155–171
Nils Bruin, Jeroen Sijsling and Alexandre Zotine
Ranks, $2$-Selmer groups, and Tamagawa numbers of elliptic curves with $\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/8\mathbb{Z}$-torsion
173–189
Stephanie Chan, Jeroen Hanselman and Wanlin Li
Counting roots for polynomials modulo prime powers
191–205
Qi Cheng, Shuhong Gao, J. Maurice Rojas and Daqing Wan
Analytic evaluation of Hecke eigenvalues for Siegel modular forms of degree two
207–220
Owen Colman, Alexandru Ghitza and Nathan C. Ryan
Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in $p$-adic cohomology
221–238
Edgar Costa, David Harvey and Kiran S. Kedlaya
On the construction of class fields
239–255
Claus Fieker, Tommy Hofmann and Carlo Sircana
Principally polarized squares of elliptic curves with field of moduli equal to $\mathbb Q$
257–274
Alexandre Gélin, Everett W. Howe and Christophe Ritzenthaler
Higher-dimensional sieving for the number field sieve algorithms
275–291
Laurent Grémy
Faster integer multiplication using short lattice vectors
293–310
David Harvey and Joris van der Hoeven
Cyclic extensions of prime degree and their $p$-adic regulators
311–323
Tommy Hofmann and Yinan Zhang
Mod-2 dihedral Galois representations of prime conductor
325–342
Kiran S. Kedlaya and Anna Medvedovsky
A new perspective on the powers of two descent for discrete logarithms in finite fields
343–352
Thorsten Kleinjung and Benjamin Wesolowski
Arithmetic statistics of Galois groups
353–374
David Kohel
A database of Belyi maps
375–392
Michael Musty, Sam Schiavone, Jeroen Sijsling and John Voight
The inverse Galois problem for $p$-adic fields
393–409
David Roe
Fast tabulation of challenge pseudoprimes
411–423
Andrew Shallue and Jonathan Webster
Fast Jacobian arithmetic for hyperelliptic curves of genus 3
425–442
Andrew V. Sutherland
A database of nonhyperelliptic genus-3 curves over $\mathbb{Q}$
443–459
Andrew V. Sutherland
Generating subgroups of ray class groups with small prime ideals
461–478
Benjamin Wesolowski
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