Edit Profile (opens in new tab) Poonen, Bjorn Co-Author Distance Author ID: poonen.bjorn Published as: Poonen, Bjorn; Poonen, B.; Poonen, Björn more...less Homepage: https://math.mit.edu/~poonen/ External Links: MGP · Wikidata · GND · IdRef · theses.fr Documents Indexed: 125 Publications since 1988, including 4 Books 6 Contributions as Editor · 1 Further Contribution Reviewing Activity: 13 Reviews Co-Authors: 102 Co-Authors with 71 Joint Publications 2,987 Co-Co-Authors all top 5 Co-Authors 60 single-authored 6 Stoll, Michael 5 Belabas, Karim 5 Coffman, Edward Grady jun. 4 Jordan, Bruce W. 4 Rains, Eric M. 4 Rodriguez-Villegas, Fernando 3 Elkies, Noam David 3 Flatto, Leopold 3 Howe, Everett W. 3 Kedlaya, Kiran Sridhara 3 Schaefer, Edward F. 2 Baker, Matthew H. 2 Bhargava, Manjul 2 Buium, Alexandru 2 Calderbank, Arthur Robert 2 Charles, François 2 Colliot-Thélène, Jean-Louis 2 Lagarias, Jeffrey C. 2 Leprévost, Franck 2 McCallum, William G. 2 Rubinstein, Michael O. 2 Shlapentokh, Alexandra 2 Slavov, Kaloyan 2 Vakil, Ravi 2 Voight, John Michael 2 Voloch, José Felipe 2 Wetherell, Joseph L. 2 Zieve, Michael E. 1 Anderson, Jacqueline 1 Balakrishnan, Jennifer S. 1 Berry, Neil 1 Beukers, Frits 1 Bleher, Frauke M. 1 Brock, Bradley W. 1 Bruin, Nils 1 Chinburg, Ted 1 Conrey, John Brian 1 Cruz-Filipe, Luís 1 Davenport, James Harold 1 de Melo, Welington 1 Dembo, Amir 1 Doyle, John R. 1 Dubickas, Artūras 1 Duursma, Iwan Maynard 1 Epstein, Adam Lawrence 1 Fan, C. Kenneth 1 Feldmann, Anja 1 Flynn, Eugene Victor 1 Gaudry, Pierrick 1 Gonzáles, Josep 1 González-Jiménez, Enrique 1 Granville, Andrew James 1 Hamblen, Spencer 1 Hassett, Brendan 1 Helfgott, Harald Andrés 1 Hrushovski, Ehud 1 Jarden, Moshe 1 Jelenković jun., Predrag 1 Kahale, Nabil 1 Kane, Daniel M. 1 Katz, Nicholas Michael 1 Keeton, Allan G. 1 Klagsbrun, Zev 1 Kresch, Andrew 1 Lenstra, Hendrik W. jun. 1 Li, Wen-Ch’ing Winnie 1 Loeser, François 1 Mallows, Colin Lingwood 1 Maulik, Davesh 1 Maynard, James 1 McGuire, Gary 1 Miller, Russell G. 1 Odlyzko, Andrew M. 1 Park, Jennifer 1 Plaxton, C. Greg 1 Poonen, George 1 Pop, Florian 1 Quasterl, Jeremy 1 Scholl, Anthony James 1 Schoutens, Hans 1 Shao, Qi-Man 1 Shepherd-Barron, Nicholas Ian 1 Siksek, Samir 1 Skinner, Christopher M. 1 Smyth, Christopher J. 1 Soundararajan, Kannan 1 Suel, Torsten 1 Sutherland, Andrew V. 1 Symonds, Peter 1 Tate, John Torrence jun. 1 Testa, Damiano 1 Tiep Pham Huu 1 Tschinkel, Yuri 1 van Luijk, Ronald M. 1 Walton, Laura 1 Watkins, Mark James 1 Winkler, Peter M. 1 Wood, Melanie Matchett 1 Wright, Margaret H. 1 Wright, Paul E. ...and 4 more Co-Authors all top 5 Serials 10 Mathematical Research Letters 7 Duke Mathematical Journal 7 Journal of the American Mathematical Society 6 Compositio Mathematica 5 IMRN. International Mathematics Research Notices 5 Annals of Mathematics. Second Series 4 Bulletin of the London Mathematical Society 4 Oberwolfach Reports 3 Acta Arithmetica 3 L’Enseignement Mathématique. 2e Série 3 Journal of the European Mathematical Society (JEMS) 2 American Mathematical Monthly 2 IEEE Transactions on Information Theory 2 Mathematics Magazine 2 American Journal of Mathematics 2 Journal of Algebra 2 Journal für die Reine und Angewandte Mathematik 2 Mathematische Annalen 2 Notices of the American Mathematical Society 2 Experimental Mathematics 2 Journal of Algebraic Geometry 2 Journal de Théorie des Nombres de Bordeaux 2 AMS/MAA Problem Books 1 Annales de l’Institut Fourier 1 Commentarii Mathematici Helvetici 1 The Fibonacci Quarterly 1 Inventiones Mathematicae 1 Journal of Combinatorial Theory. Series A 1 Journal of Number Theory 1 The Journal of Symbolic Logic 1 Mathematische Zeitschrift 1 Theoretical Computer Science 1 Journal of Algorithms 1 Ergodic Theory and Dynamical Systems 1 Probability Theory and Related Fields 1 Algorithmica 1 SIAM Journal on Discrete Mathematics 1 Forum Mathematicum 1 Journal of the Ramanujan Mathematical Society 1 The Annals of Applied Probability 1 Bulletin of the American Mathematical Society. New Series 1 Comptes Rendus de l’Académie des Sciences. Série I 1 SIAM Journal on Optimization 1 Journal of Mathematical Sciences (New York) 1 Finite Fields and their Applications 1 Documenta Mathematica 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Probability in the Engineering and Informational Sciences 1 The Quarterly Journal of Mathematics 1 Graduate Studies in Mathematics 1 Progress in Mathematics 1 Panoramas et Synthèses 1 Forum of Mathematics, Sigma 1 Cambridge Journal of Mathematics 1 Simons Symposia 1 Tunisian Journal of Mathematics all top 5 Fields 95 Number theory (11-XX) 74 Algebraic geometry (14-XX) 11 Mathematical logic and foundations (03-XX) 8 General and overarching topics; collections (00-XX) 8 Field theory and polynomials (12-XX) 7 Dynamical systems and ergodic theory (37-XX) 6 Computer science (68-XX) 4 Combinatorics (05-XX) 3 Commutative algebra (13-XX) 3 Group theory and generalizations (20-XX) 3 Probability theory and stochastic processes (60-XX) 3 Information and communication theory, circuits (94-XX) 2 Category theory; homological algebra (18-XX) 2 Real functions (26-XX) 2 Convex and discrete geometry (52-XX) 2 Operations research, mathematical programming (90-XX) 2 Mathematics education (97-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Associative rings and algebras (16-XX) 1 \(K\)-theory (19-XX) 1 Functions of a complex variable (30-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Numerical analysis (65-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 110 Publications have been cited 1,659 times in 1,333 Documents Cited by ▼ Year ▼ Bertini theorems over finite fields. Zbl 1084.14026Poonen, Bjorn 78 2005 The Cassels-Tate pairing on polarized Abelian varieties. Zbl 1024.11040Poonen, Bjorn; Stoll, Michael 70 1999 Rational points on varieties. Zbl 1387.14004Poonen, Bjorn 64 2017 Cycles of quadratic polynomials and rational points on a genus-2 curve. Zbl 0958.11024Flynn, E. V.; Poonen, Bjorn; Schaefer, Edward F. 52 1997 Zeros of polynomials with \(0, 1\) coefficients. Zbl 0814.30006Odlyzko, A. M.; Poonen, B. 49 1993 Explicit descent for Jacobians of cyclic covers of the projective line. Zbl 0888.11023Poonen, Bjorn; Schaefer, Edward F. 48 1997 Squarefree values of multivariable polynomials. Zbl 1047.11021Poonen, Bjorn 44 2003 The classification of rational preperiodic points of quadratic polynomials over \(\mathbb{Q}\): A refined conjecture. Zbl 0902.11025Poonen, Bjorn 42 1998 The method of Chabauty and Coleman. Zbl 1377.11077McCallum, William; Poonen, Bjorn 41 2012 Twists of \(X(7)\) and primitive solutions to \(x^2+y^3=z^7\). Zbl 1124.11019Poonen, Bjorn; Schaefer, Edward F.; Stoll, Michael 39 2007 Large torsion subgroups of split Jacobians of curves of genus two or three. Zbl 0983.11037Howe, Everett W.; Leprévost, Franck; Poonen, Bjorn 38 2000 A computable functor from graphs to fields. Zbl 1447.03005Miller, Russell; Poonen, Bjorn; Schoutens, Hans; Shlapentokh, Alexandra 37 2018 Random maximal isotropic subspaces and Selmer groups. Zbl 1294.11097Poonen, Bjorn; Rains, Eric 36 2012 Isomorphism types of commutative algebras of finite rank over an algebraic closed field. Zbl 1155.13015Poonen, Bjorn 35 2008 Finiteness results for modular curves of genus at least 2. Zbl 1127.11041Baker, Matthew H.; González-Jiménez, Enrique; Gonzáles, Josep; Poonen, Bjorn 34 2005 Union-closed families. Zbl 0758.05096Poonen, Bjorn 30 1992 Maximally complete fields. Zbl 0807.12006Poonen, Bjorn 30 1993 Local height functions and the Mordell-Weil theorem for Drinfeld modules. Zbl 0839.11024Poonen, Bjorn 29 1995 Hilbert’s Tenth Problem and Mazur’s Conjecture for large subrings of \(\mathbb{Q}\). Zbl 1028.11077Poonen, Bjorn 29 2003 The Grothendieck ring of varieties is not a domain. Zbl 1054.14505Poonen, Bjorn 28 2002 A heuristic for boundedness of ranks of elliptic curves. Zbl 1469.11173Park, Jennifer; Poonen, Bjorn; Voight, John; Wood, Melanie Matchett 26 2019 Random Diophantine equations. With appendices by Jean-Louis Colliot-Thélène and Nicholas M. Katz. Zbl 1208.11050Poonen, Bjorn; Voloch, José Felipe 24 2004 Random polynomials having few or no real zeros. Zbl 1002.60045Dembo, Amir; Poonen, Bjorn; Shao, Qi-Man; Zeitouni, Ofer 24 2002 Using elliptic curves of rank one towards the undecidability of Hilbert’s tenth problem over rings of algebraic integers. Zbl 1057.11068Poonen, Bjorn 24 2002 Insufficiency of the Brauer-Manin obstruction applied to étale covers. Zbl 1284.11096Poonen, Bjorn 24 2010 Mordell-Lang plus Bogomolov. Zbl 0995.11040Poonen, Bjorn 22 1999 Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves. Zbl 1329.14071Bhargava, Manjul; Kane, Daniel M.; Lenstra, Hendrik W. jun.; Poonen, Bjorn; Rains, Eric 22 2015 Heuristics for the Brauer-Manin obstruction for curves. Zbl 1173.11040Poonen, Bjorn 21 2006 Gonality of modular curves in characteristic \(p\). Zbl 1138.14016Poonen, Bjorn 20 2007 The zeta function of the beta transformation. Zbl 0843.58106Flatto, Leopold; Lagarias, Jeffrey C.; Poonen, Bjorn 20 1994 Generalized explicit descent and its application to curves of genus 3. Zbl 1408.11065Bruin, Nils; Poonen, Bjorn; Stoll, Michael 20 2016 Néron-Severi groups under specialization. Zbl 1248.14011Maulik, Davesh; Poonen, Bjorn 19 2012 Zeros of Fekete polynomials. Zbl 1007.11053Conrey, Brian; Granville, Andrew; Poonen, Bjorn; Soundararajan, K. 19 2000 Lattice polygons and the number 12. Zbl 0988.52024Poonen, Bjorn; Rodriguez-Villegas, Fernando 18 2000 Independence of points on elliptic curves arising from special points on modular and Shimura curves. II: Local results. Zbl 1232.11073Buium, Alexandru; Poonen, Bjorn 17 2009 Algebraic families of nonzero elements of Shafarevich-Tate groups. Zbl 0951.11022Colliot-Thélène, Jean-Louis; Poonen, Bjorn 17 2000 The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields. Zbl 1294.11110Poonen, Bjorn; Voloch, José Felipe 17 2010 Packing random intervals on-line. Zbl 0914.68082Coffman, E. G. jun.; Flatto, L.; Jelenković, P.; Poonen, B. 16 1998 Characterizing integers among rational numbers with a universal-existential formula. Zbl 1179.11047Poonen, Bjorn 15 2009 The moduli space of commutative algebras of finite rank. Zbl 1151.14011Poonen, Bjorn 15 2008 The number of intersection points made by the diagonals of a regular polygon. Zbl 0913.51005Poonen, Bjorn; Rubinstein, Michael 14 1998 Undecidability in number theory. Zbl 1194.03018Poonen, Bjorn 14 2008 Bertini irreducibility theorems over finite fields. Zbl 1327.14233Charles, François; Poonen, Bjorn 14 2016 Existence of rational points on smooth projective varieties. Zbl 1183.14032Poonen, Bjorn 14 2009 Diophantine definability of infinite discrete nonarchimedean sets and Diophantine models over large subrings of number field. Zbl 1139.11056Poonen, Bjorn; Shlapentokh, Alexandra 14 2005 Berkovich spaces embed in Euclidean spaces. Zbl 1325.14040Hrushovski, Ehud; Loeser, François; Poonen, Bjorn 13 2014 Most odd degree hyperelliptic curves have only one rational point. Zbl 1303.11073Poonen, Bjorn; Stoll, Michael 13 2014 An explicit algebraic family of genus-one curves violating the Hasse principle. Zbl 1046.11038Poonen, Bjorn 13 2001 Computational aspects of curves of genus at least 2. Zbl 0891.11037Poonen, Bjorn 12 1996 On a conjecture of Helleseth regarding pairs of binary \(m\)-sequences. Zbl 0943.94513Calderbank, A. R.; McGuire, Gary; Poonen, Bjorn; Rubinstein, Michael 11 1996 Smooth hypersurface sections containing a given subscheme over a finite field. Zbl 1207.14047Poonen, Bjorn 10 2008 Computing Néron-Severi groups and cycle class groups. Zbl 1316.14017Poonen, Bjorn; Testa, Damiano; van Luijk, Ronald 10 2015 A local-global principle for densities. Zbl 1024.11047Poonen, Bjorn; Stoll, Michael 10 1999 Convergence of the restricted Nelder-Mead algorithm in two dimensions. Zbl 1246.49029Lagarias, Jeffrey C.; Poonen, Bjorn; Wright, Margaret H. 10 2012 Computing torsion points on curves. Zbl 1063.11017Poonen, Bjorn 10 2001 \(p\)-adic interpolation of iterates. Zbl 1291.11135Poonen, Bjorn 9 2014 Torsion in rank 1 Drinfeld modules and the uniform boundedness conjecture. Zbl 0891.11034Poonen, Bjorn 9 1997 Automorphisms of Harbater-Katz-Gabber curves. Zbl 1372.14022Bleher, Frauke M.; Chinburg, Ted; Poonen, Bjorn; Symonds, Peter 8 2017 Some diophantine equations of the form \(x^n+y^n=z^m\). Zbl 0930.11017Poonen, Bjorn 8 1998 Varieties without extra automorphisms. II: Hyperelliptic curves. Zbl 0966.14020Poonen, Bjorn 8 2000 Curves of every genus with many points. II: Asymptotically good families. Zbl 1072.11041Elkies, Noam D.; Howe, Everett W.; Kresch, Andrew; Poonen, Bjorn; Wetherell, Joseph L.; Zieve, Michael E. 8 2004 Computing rational points on curves. Zbl 1038.11037Poonen, Bjorn 8 2002 Self cup products and the theta characteristic torsor. Zbl 1297.18005Poonen, Bjorn; Rains, Eric 7 2011 Undecidable problems: a sampler. Zbl 1358.03063Poonen, Bjorn 7 2014 Integrality and rigidity for postcritically finite polynomials. Zbl 1291.37057Epstein, Adam 7 2012 The conjugate dimension of algebraic numbers. Zbl 1062.11064Berry, Neil; Dubickas, Artūras; Elkies, Noam D.; Poonen, Bjorn; Smyth, Chris 7 2004 Varieties without extra automorphisms. III: Hypersurfaces. Zbl 1076.14053Poonen, Bjorn 7 2005 Gonality of dynatomic curves and strong uniform boundedness of preperiodic points. Zbl 1445.37080Doyle, John R.; Poonen, Bjorn 7 2020 Abelian varieties isogenous to a power of an elliptic curve. Zbl 1400.14116Jordan, Bruce W.; Keeton, Allan G.; Poonen, Bjorn; Rains, Eric M.; Shepherd-Barron, Nicholas; Tate, John T. 7 2018 First-order characterization of function field invariants over large fields. Zbl 1174.03015Poonen, Bjorn; Pop, Florian 6 2008 Packing random intervals. Zbl 0819.60013Coffman, E. G. jun.; Poonen, Bjorn; Winkler, Peter 6 1995 A 2-adic approach to the analysis of cyclic codes. Zbl 0898.94011Calderbank, A. R.; Li, Wen-Ching Winnie; Poonen, Bjorn 6 1997 Parking arcs on the circle with applications to one-dimensional communication networks. Zbl 0812.60090Coffman, E. G. jun.; Mallows, C. L.; Poonen, Bjorn 5 1994 Independence of points on elliptic curves arising from special points on modular and Shimura curves. I: Global results. Zbl 1177.11050Buium, Alexandru; Poonen, Bjorn 5 2009 Varieties without extra automorphisms. I: Curves. Zbl 0966.14019Poonen, Bjorn 5 2000 Uniform first-order definitions in finitely generated fields. Zbl 1197.12005Poonen, Bjorn 5 2007 The set of nonsquares in a number field is diophantine. Zbl 1183.14031Poonen, Bjorn 5 2009 Drinfeld modules with no supersingular primes. Zbl 0898.11024Poonen, Bjorn 4 1998 Curves over every global field violating the local-global principle. Zbl 1294.11108Poonen, B. 4 2010 Average rank of elliptic curves [after Manjul Bhargava and Arul Shankar]. Zbl 1295.11065Poonen, Bjorn 4 2013 Explicit methods in number theory. Rational points and Diophantine equations. Zbl 1267.11002Belabas, Karim; Beukers, Frits; Gaudry, Pierrick; McCallum, William; Poonen, Bjorn; Siksek, Samir; Stoll, Michael; Watkins, Mark 4 2012 The exceptional locus in the Bertini irreducibility theorem for a morphism. Zbl 1483.14097Poonen, Bjorn; Slavov, Kaloyan 4 2022 Torsion packets on curves. Zbl 0987.14020Baker, Matthew; Poonen, Bjorn 4 2001 Fractional power series and pairings on Drinfeld modules. Zbl 0861.13010Poonen, Bjorn 3 1996 Periodicity of a combinatorial sequence. Zbl 0644.10012Poonen, Bjorn 3 1988 Zeros of sparse polynomials over local fields of characteristic \(p\). Zbl 0931.11053Poonen, Bjorn 3 1998 Improved lower bounds for Shellsort. Zbl 0977.68532Plaxton, C. Greg; Poonen, Bjorn; Suel, Torsten 3 1992 Extending self-maps to projective space over finite fields. Zbl 1303.14014Poonen, Bjorn 3 2013 Automorphisms mapping a point into a subvariety. Zbl 1229.14032Poonen, Bjorn 3 2011 The Hasse principle for complete intersections in projective space. Zbl 1079.14027Poonen, Bjorn 3 2001 Unramified covers of Galois covers of low genus curves. Zbl 1082.14035Poonen, Bjorn 3 2005 Using zeta functions to factor polynomials over finite fields. Zbl 1468.11247Poonen, Bjorn 3 2019 Orbits of automorphism groups of fields. Zbl 1132.12002Kedlaya, Kiran S.; Poonen, Bjorn 3 2005 Multivariable polynomial injections on rational numbers. Zbl 1261.11030Poonen, Bjorn 2 2010 The worst case in shellsort and related algorithms. Zbl 0784.68044Poonen, Bjorn 2 1993 Computing call admission capacities in linear networks. Zbl 0969.90025Coffman, E. G. jun.; Feldmann, Anja; Kahale, Nabil; Poonen, Bjorn 2 1999 Large torsion subgroups of split Jacobians of curves of genus 2. (Sous-groupes de torsion d’ordres élevés de jacobiennes décomposables de courbes de genre 2.) Zbl 0895.11027Howe, Everett W.; Leprévost, Franck; Poonen, Bjorn 2 1996 Arithmetic of higher-dimensional algebraic varieties. Proceedings of the workshop on rational and integral points of higher-dimensional varieties, Palo Alto, CA, USA, December 11–20, 2002. Zbl 1054.11006 2 2004 Points having the same residue field as their image under a morphism. Zbl 1077.14505Poonen, Bjorn 2 2001 Spans of Hecke points on modular curves. Zbl 1081.11043Poonen, Bjorn 2 2001 The exceptional locus in the Bertini irreducibility theorem for a morphism. Zbl 1483.14097Poonen, Bjorn; Slavov, Kaloyan 4 2022 A \(p\)-adic approach to rational points on curves. Zbl 1461.11099Poonen, Bjorn 1 2021 Gonality of dynatomic curves and strong uniform boundedness of preperiodic points. Zbl 1445.37080Doyle, John R.; Poonen, Bjorn 7 2020 The analytic class number formula for 1-dimensional affine schemes. Zbl 1473.11212Jordan, Bruce W.; Poonen, Bjorn 2 2020 A heuristic for boundedness of ranks of elliptic curves. Zbl 1469.11173Park, Jennifer; Poonen, Bjorn; Voight, John; Wood, Melanie Matchett 26 2019 Using zeta functions to factor polynomials over finite fields. Zbl 1468.11247Poonen, Bjorn 3 2019 A computable functor from graphs to fields. Zbl 1447.03005Miller, Russell; Poonen, Bjorn; Schoutens, Hans; Shlapentokh, Alexandra 37 2018 Abelian varieties isogenous to a power of an elliptic curve. Zbl 1400.14116Jordan, Bruce W.; Keeton, Allan G.; Poonen, Bjorn; Rains, Eric M.; Shepherd-Barron, Nicholas; Tate, John T. 7 2018 Heuristics for the arithmetic of elliptic curves. Zbl 1443.11100Poonen, Bjorn 2 2018 Local arboreal representations. Zbl 1452.11140Anderson, Jacqueline; Hamblen, Spencer; Poonen, Bjorn; Walton, Laura 1 2018 Rational points on varieties. Zbl 1387.14004Poonen, Bjorn 64 2017 Automorphisms of Harbater-Katz-Gabber curves. Zbl 1372.14022Bleher, Frauke M.; Chinburg, Ted; Poonen, Bjorn; Symonds, Peter 8 2017 Generalized explicit descent and its application to curves of genus 3. Zbl 1408.11065Bruin, Nils; Poonen, Bjorn; Stoll, Michael 20 2016 Bertini irreducibility theorems over finite fields. Zbl 1327.14233Charles, François; Poonen, Bjorn 14 2016 Galois points on varieties. Zbl 1425.11132Jarden, Moshe; Poonen, Bjorn 1 2016 Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves. Zbl 1329.14071Bhargava, Manjul; Kane, Daniel M.; Lenstra, Hendrik W. jun.; Poonen, Bjorn; Rains, Eric 22 2015 Computing Néron-Severi groups and cycle class groups. Zbl 1316.14017Poonen, Bjorn; Testa, Damiano; van Luijk, Ronald 10 2015 Berkovich spaces embed in Euclidean spaces. Zbl 1325.14040Hrushovski, Ehud; Loeser, François; Poonen, Bjorn 13 2014 Most odd degree hyperelliptic curves have only one rational point. Zbl 1303.11073Poonen, Bjorn; Stoll, Michael 13 2014 \(p\)-adic interpolation of iterates. Zbl 1291.11135Poonen, Bjorn 9 2014 Undecidable problems: a sampler. Zbl 1358.03063Poonen, Bjorn 7 2014 Average rank of elliptic curves [after Manjul Bhargava and Arul Shankar]. Zbl 1295.11065Poonen, Bjorn 4 2013 Extending self-maps to projective space over finite fields. Zbl 1303.14014Poonen, Bjorn 3 2013 The method of Chabauty and Coleman. Zbl 1377.11077McCallum, William; Poonen, Bjorn 41 2012 Random maximal isotropic subspaces and Selmer groups. Zbl 1294.11097Poonen, Bjorn; Rains, Eric 36 2012 Néron-Severi groups under specialization. Zbl 1248.14011Maulik, Davesh; Poonen, Bjorn 19 2012 Convergence of the restricted Nelder-Mead algorithm in two dimensions. Zbl 1246.49029Lagarias, Jeffrey C.; Poonen, Bjorn; Wright, Margaret H. 10 2012 Integrality and rigidity for postcritically finite polynomials. Zbl 1291.37057Epstein, Adam 7 2012 Explicit methods in number theory. Rational points and Diophantine equations. Zbl 1267.11002Belabas, Karim; Beukers, Frits; Gaudry, Pierrick; McCallum, William; Poonen, Bjorn; Siksek, Samir; Stoll, Michael; Watkins, Mark 4 2012 Self cup products and the theta characteristic torsor. Zbl 1297.18005Poonen, Bjorn; Rains, Eric 7 2011 Automorphisms mapping a point into a subvariety. Zbl 1229.14032Poonen, Bjorn 3 2011 Insufficiency of the Brauer-Manin obstruction applied to étale covers. Zbl 1284.11096Poonen, Bjorn 24 2010 The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields. Zbl 1294.11110Poonen, Bjorn; Voloch, José Felipe 17 2010 Curves over every global field violating the local-global principle. Zbl 1294.11108Poonen, B. 4 2010 Multivariable polynomial injections on rational numbers. Zbl 1261.11030Poonen, Bjorn 2 2010 Independence of points on elliptic curves arising from special points on modular and Shimura curves. II: Local results. Zbl 1232.11073Buium, Alexandru; Poonen, Bjorn 17 2009 Characterizing integers among rational numbers with a universal-existential formula. Zbl 1179.11047Poonen, Bjorn 15 2009 Existence of rational points on smooth projective varieties. Zbl 1183.14032Poonen, Bjorn 14 2009 Independence of points on elliptic curves arising from special points on modular and Shimura curves. I: Global results. Zbl 1177.11050Buium, Alexandru; Poonen, Bjorn 5 2009 The set of nonsquares in a number field is diophantine. Zbl 1183.14031Poonen, Bjorn 5 2009 Isomorphism types of commutative algebras of finite rank over an algebraic closed field. Zbl 1155.13015Poonen, Bjorn 35 2008 The moduli space of commutative algebras of finite rank. Zbl 1151.14011Poonen, Bjorn 15 2008 Undecidability in number theory. Zbl 1194.03018Poonen, Bjorn 14 2008 Smooth hypersurface sections containing a given subscheme over a finite field. Zbl 1207.14047Poonen, Bjorn 10 2008 First-order characterization of function field invariants over large fields. Zbl 1174.03015Poonen, Bjorn; Pop, Florian 6 2008 Elliptic curves. Zbl 1214.11073Poonen, Bjorn 1 2008 Twists of \(X(7)\) and primitive solutions to \(x^2+y^3=z^7\). Zbl 1124.11019Poonen, Bjorn; Schaefer, Edward F.; Stoll, Michael 39 2007 Gonality of modular curves in characteristic \(p\). Zbl 1138.14016Poonen, Bjorn 20 2007 Uniform first-order definitions in finitely generated fields. Zbl 1197.12005Poonen, Bjorn 5 2007 Sieve methods for varieties over finite fields and arithmetic schemes. Zbl 1149.11031Poonen, Bjorn 1 2007 Heuristics for the Brauer-Manin obstruction for curves. Zbl 1173.11040Poonen, Bjorn 21 2006 Bertini theorems over finite fields. Zbl 1084.14026Poonen, Bjorn 78 2005 Finiteness results for modular curves of genus at least 2. Zbl 1127.11041Baker, Matthew H.; González-Jiménez, Enrique; Gonzáles, Josep; Poonen, Bjorn 34 2005 Diophantine definability of infinite discrete nonarchimedean sets and Diophantine models over large subrings of number field. Zbl 1139.11056Poonen, Bjorn; Shlapentokh, Alexandra 14 2005 Varieties without extra automorphisms. III: Hypersurfaces. Zbl 1076.14053Poonen, Bjorn 7 2005 Unramified covers of Galois covers of low genus curves. Zbl 1082.14035Poonen, Bjorn 3 2005 Orbits of automorphism groups of fields. Zbl 1132.12002Kedlaya, Kiran S.; Poonen, Bjorn 3 2005 Multiples of subvarieties in algebraic groups over finite fields. Zbl 1082.14028Poonen, Bjorn 2 2005 Random Diophantine equations. With appendices by Jean-Louis Colliot-Thélène and Nicholas M. Katz. Zbl 1208.11050Poonen, Bjorn; Voloch, José Felipe 24 2004 Curves of every genus with many points. II: Asymptotically good families. Zbl 1072.11041Elkies, Noam D.; Howe, Everett W.; Kresch, Andrew; Poonen, Bjorn; Wetherell, Joseph L.; Zieve, Michael E. 8 2004 The conjugate dimension of algebraic numbers. Zbl 1062.11064Berry, Neil; Dubickas, Artūras; Elkies, Noam D.; Poonen, Bjorn; Smyth, Chris 7 2004 Arithmetic of higher-dimensional algebraic varieties. Proceedings of the workshop on rational and integral points of higher-dimensional varieties, Palo Alto, CA, USA, December 11–20, 2002. Zbl 1054.11006 2 2004 Squarefree values of multivariable polynomials. Zbl 1047.11021Poonen, Bjorn 44 2003 Hilbert’s Tenth Problem and Mazur’s Conjecture for large subrings of \(\mathbb{Q}\). Zbl 1028.11077Poonen, Bjorn 29 2003 The Grothendieck ring of varieties is not a domain. Zbl 1054.14505Poonen, Bjorn 28 2002 Random polynomials having few or no real zeros. Zbl 1002.60045Dembo, Amir; Poonen, Bjorn; Shao, Qi-Man; Zeitouni, Ofer 24 2002 Using elliptic curves of rank one towards the undecidability of Hilbert’s tenth problem over rings of algebraic integers. Zbl 1057.11068Poonen, Bjorn 24 2002 Computing rational points on curves. Zbl 1038.11037Poonen, Bjorn 8 2002 The William Lowell Putnam mathematical competition 1985–2000. Problems, solutions, and commentary. Zbl 1005.00003Kedlaya, Kiran S.; Poonen, Bjorn; Vakil, Ravi 1 2002 An explicit algebraic family of genus-one curves violating the Hasse principle. Zbl 1046.11038Poonen, Bjorn 13 2001 Computing torsion points on curves. Zbl 1063.11017Poonen, Bjorn 10 2001 Torsion packets on curves. Zbl 0987.14020Baker, Matthew; Poonen, Bjorn 4 2001 The Hasse principle for complete intersections in projective space. Zbl 1079.14027Poonen, Bjorn 3 2001 Points having the same residue field as their image under a morphism. Zbl 1077.14505Poonen, Bjorn 2 2001 Spans of Hecke points on modular curves. Zbl 1081.11043Poonen, Bjorn 2 2001 Large torsion subgroups of split Jacobians of curves of genus two or three. Zbl 0983.11037Howe, Everett W.; Leprévost, Franck; Poonen, Bjorn 38 2000 Zeros of Fekete polynomials. Zbl 1007.11053Conrey, Brian; Granville, Andrew; Poonen, Bjorn; Soundararajan, K. 19 2000 Lattice polygons and the number 12. Zbl 0988.52024Poonen, Bjorn; Rodriguez-Villegas, Fernando 18 2000 Algebraic families of nonzero elements of Shafarevich-Tate groups. Zbl 0951.11022Colliot-Thélène, Jean-Louis; Poonen, Bjorn 17 2000 Varieties without extra automorphisms. II: Hyperelliptic curves. Zbl 0966.14020Poonen, Bjorn 8 2000 Varieties without extra automorphisms. I: Curves. Zbl 0966.14019Poonen, Bjorn 5 2000 Genus-two curves with 22 torsion points. Zbl 0966.11026Poonen, Bjorn 1 2000 The Cassels-Tate pairing on polarized Abelian varieties. Zbl 1024.11040Poonen, Bjorn; Stoll, Michael 70 1999 Mordell-Lang plus Bogomolov. Zbl 0995.11040Poonen, Bjorn 22 1999 A local-global principle for densities. Zbl 1024.11047Poonen, Bjorn; Stoll, Michael 10 1999 Computing call admission capacities in linear networks. Zbl 0969.90025Coffman, E. G. jun.; Feldmann, Anja; Kahale, Nabil; Poonen, Bjorn 2 1999 The classification of rational preperiodic points of quadratic polynomials over \(\mathbb{Q}\): A refined conjecture. Zbl 0902.11025Poonen, Bjorn 42 1998 Packing random intervals on-line. Zbl 0914.68082Coffman, E. G. jun.; Flatto, L.; Jelenković, P.; Poonen, B. 16 1998 The number of intersection points made by the diagonals of a regular polygon. Zbl 0913.51005Poonen, Bjorn; Rubinstein, Michael 14 1998 Some diophantine equations of the form \(x^n+y^n=z^m\). Zbl 0930.11017Poonen, Bjorn 8 1998 Drinfeld modules with no supersingular primes. Zbl 0898.11024Poonen, Bjorn 4 1998 Zeros of sparse polynomials over local fields of characteristic \(p\). Zbl 0931.11053Poonen, Bjorn 3 1998 Cycles of quadratic polynomials and rational points on a genus-2 curve. Zbl 0958.11024Flynn, E. V.; Poonen, Bjorn; Schaefer, Edward F. 52 1997 Explicit descent for Jacobians of cyclic covers of the projective line. Zbl 0888.11023Poonen, Bjorn; Schaefer, Edward F. 48 1997 Torsion in rank 1 Drinfeld modules and the uniform boundedness conjecture. Zbl 0891.11034Poonen, Bjorn 9 1997 A 2-adic approach to the analysis of cyclic codes. Zbl 0898.94011Calderbank, A. R.; Li, Wen-Ching Winnie; Poonen, Bjorn 6 1997 Computational aspects of curves of genus at least 2. Zbl 0891.11037Poonen, Bjorn 12 1996 On a conjecture of Helleseth regarding pairs of binary \(m\)-sequences. Zbl 0943.94513Calderbank, A. R.; McGuire, Gary; Poonen, Bjorn; Rubinstein, Michael 11 1996 Fractional power series and pairings on Drinfeld modules. Zbl 0861.13010Poonen, Bjorn 3 1996 Large torsion subgroups of split Jacobians of curves of genus 2. (Sous-groupes de torsion d’ordres élevés de jacobiennes décomposables de courbes de genre 2.) Zbl 0895.11027Howe, Everett W.; Leprévost, Franck; Poonen, Bjorn 2 1996 ...and 10 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,465 Authors 36 Poonen, Bjorn 18 Stoll, Michael 17 Shlapentokh, Alexandra 14 Fisher, Tom A. 14 Miller, Russell G. 13 Creutz, Brendan 12 Viray, Bianca 11 Balakrishnan, Jennifer S. 11 Bhargava, Manjul 11 Flynn, Eugene Victor 11 Kedlaya, Kiran Sridhara 10 Erdélyi, Tamás 10 Loughran, Daniel 10 Pasten, Hector V. 10 Voloch, José Felipe 9 Bazhenov, Nikolaĭ Alekseevich 9 Buium, Alexandru 9 Doyle, John R. 9 Ghioca, Dragos 9 Siksek, Samir 8 Wood, Melanie Matchett 7 Borwein, Peter Benjamin 7 Cornelissen, Gunther 7 González, Josep R. 7 Howe, Everett W. 7 Ishitsuka, Yasuhiro 7 Katz, Daniel J. 7 Liu, Qing 7 Mazur, Barry 7 Müller, Jan Steffen 7 Silverman, Joseph Hillel 6 Browning, Timothy Daniel 6 Bruin, Nils 6 Cao, Yang 6 Cremona, John E. 6 Freitas, Nuno 6 Harrison-Trainor, Matthew 6 Ingram, Patrick 6 Liang, Yongqi 6 Ritzenthaler, Christophe 6 Rojas, J. Maurice 6 Schaefer, Edward F. 6 Shparlinski, Igor E. 6 Várilly-Alvarado, Anthony 5 Bars Cortina, Francesc 5 Bennett, Michael A. 5 Berenhaut, Kenneth S. 5 Colliot-Thélène, Jean-Louis 5 Elias, Joan 5 Fehm, Arno 5 Ito, Tetsushi 5 Krumm, David 5 Langevin, Philippe 5 Li, Wanlin 5 Lorenzini, Dino J. 5 Lorenzo García, Elisa 5 Manes, Michelle 5 Melnikov, Alexander G. 5 Micheli, Giacomo 5 Nakahara, Masahiro 5 Sutherland, Andrew V. 5 Voight, John Michael 5 Xue, Jiangwei 5 Zarkhin, Yuriĭ Gennad’evich 5 Zureick-Brown, David 4 Asgarli, Shamil 4 Benedetto, Robert L. 4 Bruhn, Henning 4 Casnati, Gianfranco 4 Castryck, Wouter 4 Česnavičius, Kęstutis 4 Clark, Peter Louis 4 David, Chantal 4 Dembo, Amir 4 Faber, Xander 4 Favre, Charles 4 González-Jiménez, Enrique 4 Habegger, Philipp 4 Hare, Kevin G. 4 Hindes, Wade 4 Hirakawa, Yoshinosuke 4 Ho, Wei 4 Homs Pons, Roser 4 Hutz, Benjamin 4 Joshi, Vinayak V. 4 Kaplan, Nathan 4 Keller, Timo 4 Knight, Julia F. 4 König, Joachim 4 Le Boudec, Pierre 4 Panin, Ivan A. 4 Park, Jennifer 4 Pries, Rachel J. 4 Rhee, Wansoo T. 4 Rubin, Karl Cooper 4 Sharif, Shahed 4 Sijsling, Jeroen 4 Sofos, Efthymios 4 Stein, William A. 4 Sun, Chia-Liang ...and 1,365 more Authors all top 5 Cited in 250 Serials 101 Journal of Number Theory 47 Mathematics of Computation 44 Transactions of the American Mathematical Society 40 Advances in Mathematics 39 Journal of Algebra 39 Journal de Théorie des Nombres de Bordeaux 33 Compositio Mathematica 33 International Journal of Number Theory 32 Proceedings of the American Mathematical Society 30 Duke Mathematical Journal 27 Mathematische Annalen 24 Journal of Pure and Applied Algebra 24 Research in Number Theory 21 Algebra & Number Theory 18 Mathematical Proceedings of the Cambridge Philosophical Society 18 Manuscripta Mathematica 17 Annals of Mathematics. 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International Mathematics Research Notices 3 The Journal of Geometric Analysis 3 Designs, Codes and Cryptography 3 Archive for Mathematical Logic 3 Applicable Algebra in Engineering, Communication and Computing 3 Izvestiya: Mathematics 3 Algebraic & Geometric Topology 3 Journal of the Australian Mathematical Society 3 Journal of Algebra and its Applications 3 Proceedings of the Steklov Institute of Mathematics 3 SIAM Journal on Applied Algebra and Geometry 2 Advances in Applied Probability 2 American Mathematical Monthly 2 Discrete Applied Mathematics 2 Indian Journal of Pure & Applied Mathematics ...and 150 more Serials all top 5 Cited in 54 Fields 811 Number theory (11-XX) 660 Algebraic geometry (14-XX) 93 Mathematical logic and foundations (03-XX) 86 Dynamical systems and ergodic theory (37-XX) 74 Field theory and polynomials (12-XX) 72 Combinatorics (05-XX) 68 Commutative algebra (13-XX) 65 Probability theory and stochastic processes (60-XX) 52 Group theory and generalizations (20-XX) 40 Functions of a complex variable (30-XX) 29 Computer science (68-XX) 26 Several complex variables and analytic spaces (32-XX) 26 Information and communication theory, circuits (94-XX) 25 Real functions (26-XX) 21 Associative rings and algebras (16-XX) 20 Linear and multilinear algebra; matrix theory (15-XX) 19 Convex and discrete geometry (52-XX) 18 Operations research, mathematical programming (90-XX) 17 Order, lattices, ordered algebraic structures (06-XX) 14 Numerical analysis (65-XX) 13 \(K\)-theory (19-XX) 13 Algebraic topology (55-XX) 12 Nonassociative rings and algebras (17-XX) 11 Geometry (51-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 10 Differential geometry (53-XX) 8 Topological groups, Lie groups (22-XX) 8 Manifolds and cell complexes (57-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 Category theory; homological algebra (18-XX) 7 Quantum theory (81-XX) 6 General and overarching topics; collections (00-XX) 6 Measure and integration (28-XX) 5 History and biography (01-XX) 5 Partial differential equations (35-XX) 5 Approximations and expansions (41-XX) 5 Functional analysis (46-XX) 4 Special functions (33-XX) 3 General algebraic systems (08-XX) 3 Ordinary differential equations (34-XX) 2 Potential theory (31-XX) 2 Difference and functional equations (39-XX) 2 Operator theory (47-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Statistics (62-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General topology (54-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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