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Improvements in the computation of ideal class groups of imaginary quadratic number fields
Explicit 2-power torsion of genus 2 curves over finite fields
1. | Departament de Matemàtica, Universitat de Lleida, Jaume II 69, Lleida 25001, Spain, Spain |
2. | Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Jordi Girona 1–3, Barcelona 08134, Spain |
[1] |
Josep M. Miret, Jordi Pujolàs, Nicolas Thériault. Trisection for supersingular genus $2$ curves in characteristic $2$. Advances in Mathematics of Communications, 2014, 8 (4) : 375-387. doi: 10.3934/amc.2014.8.375 |
[2] |
Peter Birkner, Nicolas Thériault. Efficient halving for genus 3 curves over binary fields. Advances in Mathematics of Communications, 2010, 4 (1) : 23-47. doi: 10.3934/amc.2010.4.23 |
[3] |
Stefan Erickson, Michael J. Jacobson, Jr., Andreas Stein. Explicit formulas for real hyperelliptic curves of genus 2 in affine representation. Advances in Mathematics of Communications, 2011, 5 (4) : 623-666. doi: 10.3934/amc.2011.5.623 |
[4] |
Stefania Fanali, Massimo Giulietti, Irene Platoni. On maximal curves over finite fields of small order. Advances in Mathematics of Communications, 2012, 6 (1) : 107-120. doi: 10.3934/amc.2012.6.107 |
[5] |
Joseph H. Silverman. Local-global aspects of (hyper)elliptic curves over (in)finite fields. Advances in Mathematics of Communications, 2010, 4 (2) : 101-114. doi: 10.3934/amc.2010.4.101 |
[6] |
David Aulicino, Chaya Norton. Shimura–Teichmüller curves in genus 5. Journal of Modern Dynamics, 2020, 16: 255-288. doi: 10.3934/jmd.2020009 |
[7] |
Ryutaroh Matsumoto. Strongly secure quantum ramp secret sharing constructed from algebraic curves over finite fields. Advances in Mathematics of Communications, 2019, 13 (1) : 1-10. doi: 10.3934/amc.2019001 |
[8] |
Ferruh Özbudak, Burcu Gülmez Temür, Oǧuz Yayla. Further results on fibre products of Kummer covers and curves with many points over finite fields. Advances in Mathematics of Communications, 2016, 10 (1) : 151-162. doi: 10.3934/amc.2016.10.151 |
[9] |
Shiliang Weng, Xiang Zhang. Integrability of vector fields versus inverse Jacobian multipliers and normalizers. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 6539-6555. doi: 10.3934/dcds.2016083 |
[10] |
Michael Braun, Michael Kiermaier, Reinhard Laue. New 2-designs over finite fields from derived and residual designs. Advances in Mathematics of Communications, 2019, 13 (1) : 165-170. doi: 10.3934/amc.2019010 |
[11] |
Nazar Arakelian, Saeed Tafazolian, Fernando Torres. On the spectrum for the genera of maximal curves over small fields. Advances in Mathematics of Communications, 2018, 12 (1) : 143-149. doi: 10.3934/amc.2018009 |
[12] |
Rodrigo Abarzúa, Nicolas Thériault, Roberto Avanzi, Ismael Soto, Miguel Alfaro. Optimization of the arithmetic of the ideal class group for genus 4 hyperelliptic curves over projective coordinates. Advances in Mathematics of Communications, 2010, 4 (2) : 115-139. doi: 10.3934/amc.2010.4.115 |
[13] |
Florian Luca, Igor E. Shparlinski. On finite fields for pairing based cryptography. Advances in Mathematics of Communications, 2007, 1 (3) : 281-286. doi: 10.3934/amc.2007.1.281 |
[14] |
Isaac A. García, Jaume Giné. Non-algebraic invariant curves for polynomial planar vector fields. Discrete and Continuous Dynamical Systems, 2004, 10 (3) : 755-768. doi: 10.3934/dcds.2004.10.755 |
[15] |
Francisco Braun, José Ruidival dos Santos Filho. The real jacobian conjecture on $\R^2$ is true when one of the components has degree 3. Discrete and Continuous Dynamical Systems, 2010, 26 (1) : 75-87. doi: 10.3934/dcds.2010.26.75 |
[16] |
Wouter Castryck, Marco Streng, Damiano Testa. Curves in characteristic $2$ with non-trivial $2$-torsion. Advances in Mathematics of Communications, 2014, 8 (4) : 479-495. doi: 10.3934/amc.2014.8.479 |
[17] |
Igor E. Shparlinski. On some dynamical systems in finite fields and residue rings. Discrete and Continuous Dynamical Systems, 2007, 17 (4) : 901-917. doi: 10.3934/dcds.2007.17.901 |
[18] |
Jean-François Biasse, Michael J. Jacobson, Jr.. Smoothness testing of polynomials over finite fields. Advances in Mathematics of Communications, 2014, 8 (4) : 459-477. doi: 10.3934/amc.2014.8.459 |
[19] |
Robert Granger, Thorsten Kleinjung, Jens Zumbrägel. Indiscreet logarithms in finite fields of small characteristic. Advances in Mathematics of Communications, 2018, 12 (2) : 263-286. doi: 10.3934/amc.2018017 |
[20] |
Shengtian Yang, Thomas Honold. Good random matrices over finite fields. Advances in Mathematics of Communications, 2012, 6 (2) : 203-227. doi: 10.3934/amc.2012.6.203 |
2020 Impact Factor: 0.935
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