Vol. 1, No. 1, 2013
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Proceedings of the Tenth Algorithmic Number Theory Symposium
Edited by Everett W. Howe and Kiran S. Kedlaya
DOI:
10.2140/obs.2013.1-1
Contents
Preface
7–9
Everett W. Howe and Kiran S. Kedlaya
Deterministic elliptic curve primality proving for a special sequence of numbers
1–20
Alexander Abatzoglou, Alice Silverberg, Andrew V. Sutherland and Angela Wong
Imaginary quadratic fields with isomorphic abelian Galois groups
21–39
Athanasios Angelakis and Peter Stevenhagen
Iterated Coleman integration for hyperelliptic curves
41–61
Jennifer S. Balakrishnan
Finding ECM-friendly curves through a study of Galois properties
63–86
Razvan Barbulescu, Joppe W. Bos, Cyril Bouvier, Thorsten Kleinjung and Peter L. Montgomery
Two grumpy giants and a baby
87–111
Daniel J. Bernstein and Tanja Lange
Improved techniques for computing the ideal class group and a system of fundamental units in number fields
113–133
Jean-François Biasse and Claus Fieker
Conditionally bounding analytic ranks of elliptic curves
135–144
Jonathan W. Bober
A database of elliptic curves over ${\mathbb Q}(\sqrt{5})$: a first report
145–166
Jonathan Bober, Alyson Deines, Ariah Klages-Mundt, Benjamin LeVeque, R. Andrew Ohana, Ashwath Rabindranath, Paul Sharaba and William Stein
Finding simultaneous Diophantine approximations with prescribed quality
167–185
Wieb Bosma and Ionica Smeets
Success and challenges in determining the rational points on curves
187–212
Nils Bruin
Solving quadratic equations in dimension $5$ or more without factoring
213–233
Pierre Castel
Counting value sets: algorithm and complexity
235–248
Qi Cheng, Joshua E. Hill and Daqing Wan
Haberland's formula and numerical computation of Petersson scalar products
249–270
Henri Cohen
Approximate common divisors via lattices
271–293
Henry Cohn and Nadia Heninger
Explicit descent in the Picard group of a cyclic cover of the projective line
295–315
Brendan Creutz
Computing equations of curves with many points
317–334
Virgile Ducet and Claus Fieker
Computing the unit group, class group, and compact representations in algebraic function fields
335–358
Kirsten Eisenträger and Sean Hallgren
The complex polynomials $P(x)$ with $\mathop{\rm Gal}(P(x)-t) \cong M_{23}$
359–367
Noam D. Elkies
Experiments with the transcendental Brauer-Manin obstruction
369–394
Andreas-Stephan Elsenhans and Jörg Jahnel
Explicit $5$-descent on elliptic curves
395–411
Tom Fisher
On the density of abelian surfaces with Tate-Shafarevich group of order five times a square
413–435
Stefan Keil and Remke Kloosterman
Improved CRT algorithm for class polynomials in genus $2$
437–461
Kristin E. Lauter and Damien Robert
Fast computation of isomorphisms of hyperelliptic curves and explicit Galois descent
463–486
Reynald Lercier, Christophe Ritzenthaler and Jeroen Sijsling
Elliptic factors in Jacobians of hyperelliptic curves with certain automorphism groups
487–505
Jennifer Paulhus
Isogeny volcanoes
507–530
Andrew V. Sutherland
On the evaluation of modular polynomials
531–555
Andrew V. Sutherland
Constructing and tabulating dihedral function fields
557–585
Colin Weir, Renate Scheidler and Everett W. Howe
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