Math Drafts of Francesc Bars

Publications

Francesc Bars: Bielliptic modular curves.
J. Number Theory 76 (1999), no. 1, 154—165 11G18 (11G30) .

-briefly version (abstract in French) 5 pages.(pdf file comrencomren-UAB)
-extended version (in catalan language) 86 pages, Prize Evariste Galois 1998 -( pdf file Tesina Tesina-UAB)

Francesc Bars: On the Tamagawa number conjecture.

Thesis UAB, may 2001. Publicacions de la Universitat Autònoma de Barcelona,

2002. Published also on line under http://www.tdcat.cesca.es/TDCat-1211101-102742

Francesc Bars: On the Tamagawa number conjecture for CM elliptic curves defined over Q.

J. Number Theory 95 (2002), no. 2, 190--208. 11G15 (11G05).

Francesc Bars: A relation between p-adic L-functions and the Tamagawa number conjecture for Hecke characters.
Archiv der Mathematik (Basel) 83,(2004), 317-327. 11G40 (11G55, 11R23,19F27)

Francesc Bars and Luis Dieulefait: Galois actions on Q-curves and Winding Quotients. Math.Zeit. (2006), published the 25 May on line (old pdf file)

Francesc Bars: On Jannsen's conjecture for Hecke character of imaginary quadratic fields. Proceedings of the Primeras Jornadas de Teoria de Números, Vilanova i la Geltrú. Publ.Mat. 2007, volum extra, 29-42, (2007):(pdf file).

Francesc Bars: The group structure of the normalizer of $\Gamma_0(N)$ after Atkin-Lehner. Communications in Algebra 36, No. 6, 2160-2170 (2008).(old pdf file)

Francesc Bars: Weak Leopoldt's conjecture for Hecke character of imaginary quadratic fields. Preprint number 23 UAB Math Department, July 2005. Reviewed version November 2005 :(old pdf file). Journal of Algebra 319, No.5, 1954-1970 (2008).

Francesc Bars and Ignazio Longhi: Reciprocity laws à la Iwasawa-Wiles. October 2007. Revised, August 2008(pdf file). Library of the Rev. Mat. Iberomericana. Proceedings of the Segundas Jornadas de Teoría de Números, Madrid, 2008.

Francesc Bars and Ignazio Longhi: Coleman's power series and Wiles' reciprocity for Drinfeld modules. Journal of Number Theory 129, No.4, 789-805 (2009) (old pdf file).

Francesc Bars: On the Tamagawa number conjecture for Hecke characters. Math. Nachr. 284 (2011), no. 5-6, 608–628.(old pdf file)

Francesc Bars: On the automorphisms groups of genus 3 curves. Surveys in Math. and Math. Sciences, vol.2.n.2, (2012), 83-124. (see old seminar file)

Francesc Bars, Aristides Kontogeorgis and Xavier Xarles: Hyperelliptic and bielliptic modular curves X(N) and the group Aut(X(N)). Acta Arithmetica 161, No. 3, 283-299 (2013).(old pdf file)

Andrea Bandini, Francesc Bars, Ignazio Longhi: Characteristic ideals and Iwasawa theory. New York Journal of Mathematics, vol. 20 (2014), 759-778. (pdf file)

Francesc Bars: On non-noetherian Iwasawa theory. Appendix in the paper of David Burns and Fabien Trihan : On geometric Iwasawa theory and special values of Zeta-functions in the book Arithmetic Geometry over Global Function Fields , Advanced Courses in Mathematics-CRM Barcelona, Birkhaeusser, (2014),119--181.

Andrea Bandini, Francesc Bars, Ignazio Longhi: Characteristic ideals and Selmer groups. Journal of Number Theory, vol. 157 (2015), 530-546. (old pdf file)

Eslam Badr, Francesc Bars: Non-singular plane curves with an element of ``large'' order in its automorphism group. International Journal of Algebra and Computation, vol. 26, issue 02, 399-434, March 2016. (old pdf file)

Eslam Badr, Francesc Bars: Automorphism groups of non-singular plane curves of degree 5. Communications in Algebra 44, 4327-4340, 2016. (old pdf file)

Eslam Badr, Francesc Bars: On the locus of smooth plane curves with a fixed automorphism group. Mediterr. J. Math. 13 (2016), no. 5, 3605–-3627. (old pdf file)

Francesc Bars: On quadratic points of classical modular curves. Contemporary Mathematics, Momose memorial Volume, Vol. 701, 17--34, (2018). (old pdf file)

Eslam Badr, Francesc Bars, Elisa Lorenzo: The Picard Group of Brauer-Severi Varieties . Open Mathematics, de Gruyter (2018); volume 16: 1196–1203 (pdf file)

Eslam Badr, Francesc Bars, Elisa Lorenzo: On twists of smooth plane curves. Math. Comp. 88 (2019), 421--438, DOI: https://doi.org/10.1090/mcom/3317. (old pdf file)

Eslam Badr, Francesc Bars: Plane model-fields of definition, fields of definition, the field of moduli of smooth plane curves . Journal of Number Theory 194 (2019) 278-–283, DOI:https://doi.org/10.1016/j.jnt.2018.07.010. (old pdf file)

Francesc Bars, Josep González: Bielliptic modular curves X^*_0(N) with square-free levels. Math. Comp. 88 (2019), 2939-2957, DOI: https://doi.org/10.1090/mcom/3424. (old pdf file)

Andrea Bandini, Francesc Bars, Ignazio Longhi: Aspects of Iwasawa theory over function fields. Preprint revised,research article, pp.375--415 in the book.(old pdf file) $t$-Motives: Hodge Structures, Transcendence and Other Motivic Aspects EMS Series of Congress Reports.. ISBN print 978-3-03719-198-9, ISBN online 978-3-03719-698-4 DOI 10.4171/198 May 2020, 473 pages.

Bruno Anglès, Andrea Bandini, Francesc Bars, Ignazio Longhi: Iwasawa main conjecture for the Carlitz cyclotomic extension and applications. Math. Ann. 376, No. 1-2, 475-523 (2020). https://doi.org/10.1007/s00208-019-01875-8 (old pdf file)

Eslam Badr, Francesc Bars:Hypersurface model-fields of definition for smooth hypersurfaces and their twists. Acta Arithmetica 194 (2020), 267-280; DOI: 10.4064/aa180524-31-7 10.4064/aa180524-31-7. (old pdf file)

Francesc Bars, Josep González: Bielliptic modular curves X^*_0(N). Journal of Algebra,Volume 559, 1 October 2020, Pages 726-759, https://doi.org/10.1016/j.jalgebra.2020.02.028. (old pdf file)

F. Bars, J.González, M.Kamel: Bielliptic quotient curves of modular curves X_0(N) with square-free levels. Journal of Number Theory, Volume 216, November 2020, Pages 380-402,https://doi.org/10.1016/j.jnt.2020.03.010 (old pdf file)

F. Bars, J.González, X.Xarles: Hyperelliptic parametrizations of Q-curves. Ramanujan J. 56 (2021), no. 1, 103–-120, 10.1007/s11139-020-00281-y. (old pdf file)

Eslam Badr, Francesc Bars: Bielliptic smooth plane curves and quadratic points. . Int. J. Number Theory 17 (2021), no. 4, 1047–1066. DOI: 10.1142/S1793042121500238 (old pdf file)

Francesc Bars, Josep González: The automorphism group of the modular curve $X_0^*(N)$ with square-free levels. Trans. Amer. Math. Soc. 374 (2021), 5783-5803 (pdf old file)

Andrea Bandini, Francesc Bars, Eduardo Coscelli: Fitting ideals of Class groups in Carlitz-Hayes cyclotomic extensions. J. Number Theory 232 (2022), 261–282. https://doi.org/10.1016/j.jnt.2018.12.010.(old pdf file)

F. Bars, M.Kamel, A. Schweizer: Bielliptic quotient curves of X_0(N). Mathematics of Computation AMS Volume 92, Number 340, (2023), Pages 895–929 https://doi.org/10.1090/mcom/3800 (old pdf file)

F. Bars, T. Dalal: Infinitely many cubic points for X_0^+(N) over Q. Acta Arithmetica. To appear in (2023) (online first version)

E. Badr, F. Bars: On fake ES-irreducible components of certain strata of smooth plane sextics. Accepted to publish August 2023, Journal of Algebra and its Applications.https://doi.org/10.1142/S0219498825500483 (old pdf file)

Pre-Publications

E. Badr, F. Bars: The stratification by automorphism groups of smooth plane sextic curves. Preprint, August 2022, submitted. (old pdf file)

F. Bars: On Hecke groups. Work in progress, April 2020.

F. Bars, J.C.Lario: Diophantine stability for curves over finite fields. Manuscript, September 2023. (old pdf file)

F. Bars, T.Dalal: Automorphism group of quotient curves $X_0(pq)$. Manuscript, September 2023. (old pdf file)

Francesc Bars, Josep González: Some Magma sources useful for the papers on bielliptic X^*_0(N)
For N square-free: to compute points of a finite field for X^*_0(N) and the implementation of Gonzalez algorithm concerning triviallity of automorfisme group of a smooth plane curve over finite field, ... (Magma source)
For N general, to compute the numberof fixed points by a Atkin-Lehner involution of X_0(N), and the genus of the quotients of X_0(N) by a subgroup generated by certain Atkin-Lehner involutions (Magma source)

Francesc Bars: Magma functions sources, and Mathematica files useful for the papers on biellipticity for quotient modular curves X_0(N)/W_N
(github folders on quotient modular curves)

Francesc Bars, Ignazio Longhi: Coleman power series for elliptic units in global function fields. Manuscript, May 2010.

Publications for mathematicians

Pere Ara i Francesc Bars: Bicentenari d'un revolucionari: Evariste Galois. . Materials Matemàtics, Revista Electrònica de Divulgació Matemàtica Editada pel Departament de Matemàtiques de la Universitat Autònoma de Barcelona, Barcelona 2012. Fitxer pdf (in catalan language).

Francesc Bars: Las medallas Fields: Vladimir Drinfeld. La Gaceta de la RSME, vol. 20 (2017), págs 171-192 . Fitxer pdf (in castilian language).

Seminar Notes

Francesc Bars: Automorphic L functions (I). Notes del Seminari de Teoria de Nombres (STNB) UB-UAB-UPC: Automorphic representations of GL(2). Barcelona 1997, ISBN 84-923250-2-X. Fitxer dvi (in catalan language).

Francesc Bars: Birch-Swinnerton-Dyer conjecture for function fields. Notes del Seminari de Teoria Nombres UB-UAB-UPC 2001/02: Drinfeld modules. Barcelona, Febrer 2002. Fitxer pdf (in catalan language).

Francesc Bars: Fontaine-Mazur conjecture. Notes del Seminari de Teoria Nombres UB-UAB-UPC 2003/04: Galois representations of dimension 2. Barcelona, Gener 2004. Fitxer pdf (in catalan language).

Francesc Bars: On the automorphisms groups of genus 3 curves. Notes del Seminari de Teoria Nombres UB-UAB-UPC 2004/05: Genus 3 curves. Barcelona, Gener 2005. Published in revised form in SMMS, vol.2, 2012, p.83-124. Pdf seminar file (in english).

Supervised PhD theses

Eslam Badr (Eslam Ebrahim Essam Farag): On the stratification of smooth plane curves by automorphism groups. PhD defended Setember 2017 at UAB.Thesis on line UAB

Supervised Bachelor theses

Jordi Ribes González: La formulació de la conjectura de Birch i Swinnerton-Dyer, un dels problemes del mil.leni de l'Institut Clay. Bellaterra, setembre 2011. Fitxer pdf (in catalan language).

Miquel Raïch Regué: La funció zeta de Riemann, diverses maravelles de la funció. Bellaterra, setembre 2011. Fitxer pdf (in catalan language).

Jone Uria Albizuri: Correspondència bijectiva de Galois en extensions no finites. Bellaterra, juny 2012. Fitxer pdf (in catalan language).

David Bachiller Pérez: La funció zeta de Carlitz-Goss: un anàleg de la funció zeta en característica positiva. Bellaterra, juny 2012. Fitxer pdf (in catalan language).

Niels Gleining: On the critical strip of the Riemann zeta function. Bellaterra, juny 2014. Fitxer pdf .

Isaac Aarón Jesús Lorenzo: Invariantes de Iwasawa en Z_p-extensiones. Bellaterra, juny 2018. Fitxer pdf (in castillian language).

Laura Soler Riba: Sobre extensions abelianes de F_p(T). Bellaterra, setembre 2018. Fitxer pdf (in catalan language).

Sergi Arjó Segovia: Grup de classes d'ideals sobre cossos globals. Exemples en extensions ciclotòmiques i teorema de Stickelberger. Bellaterra, juliol 2021. Fitxer pdf (in catalan language).

Jordi Gual Tallero: Sobre la fórmula del residu i fórmules del nombre de classe. Bellaterra, juliol 2022. Fitxer pdf (in catalan language).

Helena Vila Crespo: Sobre formes quadràtiques binàries i grup de classes. Bellaterra, juliol 2022. Fitxer pdf (in catalan language).

Niels Knudsen Esquerra: The genus formula for the Carlitz cyclotomic extension. Bellaterra, juliol 2022. Fitxer pdf (in catalan language).

Habib Ullah Abdul Parveen: Analogues of Fermat equation in the arithmetic of rational function fields over a finite field. Bellaterra, setembre 2022. Fitxer pdf (in catalan language).

Fernando Alaejos García: Carlitz exponential: on the analogs of the numbers e and pi for rational function fields over finite fields. Bellaterra, setembre 2022. Fitxer pdf (in catalan language).

David Olivar Lacambra: Sobre punts de torsió de mòduls de Drinfeld de rang 2. Bellaterra, juliol 2023. Fitxer pdf (in catalan language).