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 Videos: carmin.tv Documents Indexed: 138 Publications since 1988, including 4 Books and 11 Additional arXiv Preprints 6 Contributions as Editor · 1 Further Contribution Reviewing Activity: 13 Reviews Biographic References: 1 Publication Co-Authors: 115 Co-Authors with 80 Joint Publications 3,482 Co-Co-Authors all top 5 Co-Authors 64 single-authored 7 Stoll, Michael 5 Belabas, Karim 5 Coffman, Edward Grady jun. 5 Jordan, Bruce W. 4 Kedlaya, Kiran Sridhara 4 Rains, Eric M. 4 Rodriguez-Villegas, Fernando 3 Elkies, Noam David 3 Flatto, Leopold 3 Howe, Everett W. 3 Rubinstein, Michael O. 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 Cruz-Filipe, Luís 2 Davenport, James Harold 2 Helfgott, Harald Andrés 2 Keeton, Allan G. 2 Lagarias, Jeffrey C. 2 Leprévost, Franck 2 Maynard, James 2 McCallum, William G. 2 Pop, Florian 2 Shlapentokh, Alexandra 2 Slavov, Kaloyan 2 Tiep Pham Huu 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 Bary-Soroker, Lior 1 Berg, Jennifer 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 Costa, Edgar 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 Hokken, David 1 Hrushovski, Ehud 1 Jarden, Moshe 1 Jelenković jun., Predrag 1 Kahale, Nabil 1 Kane, Daniel M. 1 Katz, Nicholas Michael 1 Klagsbrun, Zev 1 Kozma, Gady 1 Kresch, Andrew 1 Landesman, Aaron 1 Lenstra, Hendrik W. jun. 1 Li, Wanlin 1 Li, Wen-Ch’ing Winnie 1 Loeser, François 1 Mallows, Colin Lingwood 1 Maulik, Davesh 1 McGuire, Gary 1 Miller, Russell G. 1 Odlyzko, Andrew M. 1 Pagano, Carlo 1 Park, Jennifer 1 Plaxton, C. Greg 1 Poonen, George 1 Quasterl, Jeremy 1 Rybakov, Sergeĭ Yur’evich 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. ...and 17 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 Bulletin of the London Mathematical Society 5 IMRN. International Mathematics Research Notices 5 Annals of Mathematics. Second Series 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 105 Number theory (11-XX) 81 Algebraic geometry (14-XX) 12 Mathematical logic and foundations (03-XX) 8 General and overarching topics; collections (00-XX) 8 Field theory and polynomials (12-XX) 8 Dynamical systems and ergodic theory (37-XX) 6 Computer science (68-XX) 4 Combinatorics (05-XX) 4 Group theory and generalizations (20-XX) 3 Commutative algebra (13-XX) 3 Convex and discrete geometry (52-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 Geometry (51-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 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Calculus of variations and optimal control; optimization (49-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 115 Publications have been cited 1,967 times in 1,562 Documents Cited by ▼ Year ▼ Rational points on varieties. Zbl 1387.14004 Poonen, Bjorn 101 2017 The Cassels-Tate pairing on polarized Abelian varieties. Zbl 1024.11040 Poonen, Bjorn; Stoll, Michael 84 1999 Bertini theorems over finite fields. Zbl 1084.14026 Poonen, Bjorn 84 2005 Cycles of quadratic polynomials and rational points on a genus-2 curve. Zbl 0958.11024 Flynn, E. V.; Poonen, Bjorn; Schaefer, Edward F. 60 1997 Zeros of polynomials with \(0, 1\) coefficients. Zbl 0814.30006 Odlyzko, A. M.; Poonen, B. 55 1993 Squarefree values of multivariable polynomials. Zbl 1047.11021 Poonen, Bjorn 53 2003 The method of Chabauty and Coleman. Zbl 1377.11077 McCallum, William; Poonen, Bjorn 53 2012 Explicit descent for Jacobians of cyclic covers of the projective line. Zbl 0888.11023 Poonen, Bjorn; Schaefer, Edward F. 51 1997 Large torsion subgroups of split Jacobians of curves of genus two or three. Zbl 0983.11037 Howe, Everett W.; Leprévost, Franck; Poonen, Bjorn 50 2000 The classification of rational preperiodic points of quadratic polynomials over \(\mathbb{Q}\): A refined conjecture. Zbl 0902.11025 Poonen, Bjorn 49 1998 Twists of \(X(7)\) and primitive solutions to \(x^2+y^3=z^7\). Zbl 1124.11019 Poonen, Bjorn; Schaefer, Edward F.; Stoll, Michael 43 2007 Random maximal isotropic subspaces and Selmer groups. Zbl 1294.11097 Poonen, Bjorn; Rains, Eric 43 2012 Isomorphism types of commutative algebras of finite rank over an algebraic closed field. Zbl 1155.13015 Poonen, Bjorn 40 2008 A computable functor from graphs to fields. Zbl 1447.03005 Miller, Russell; Poonen, Bjorn; Schoutens, Hans; Shlapentokh, Alexandra 40 2018 A heuristic for boundedness of ranks of elliptic curves. Zbl 1469.11173 Park, Jennifer; Poonen, Bjorn; Voight, John; Wood, Melanie Matchett 37 2019 Finiteness results for modular curves of genus at least 2. Zbl 1127.11041 Baker, Matthew H.; González-Jiménez, Enrique; Gonzáles, Josep; Poonen, Bjorn 36 2005 Maximally complete fields. Zbl 0807.12006 Poonen, Bjorn 34 1993 Local height functions and the Mordell-Weil theorem for Drinfeld modules. Zbl 0839.11024 Poonen, Bjorn 32 1995 Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves. Zbl 1329.14071 Bhargava, Manjul; Kane, Daniel M.; Lenstra, Hendrik W. jun.; Poonen, Bjorn; Rains, Eric 32 2015 Using elliptic curves of rank one towards the undecidability of Hilbert’s tenth problem over rings of algebraic integers. Zbl 1057.11068 Poonen, Bjorn 31 2002 Union-closed families. Zbl 0758.05096 Poonen, Bjorn 30 1992 Hilbert’s Tenth Problem and Mazur’s Conjecture for large subrings of \(\mathbb{Q}\). Zbl 1028.11077 Poonen, Bjorn 30 2003 The Grothendieck ring of varieties is not a domain. Zbl 1054.14505 Poonen, Bjorn 29 2002 Insufficiency of the Brauer-Manin obstruction applied to étale covers. Zbl 1284.11096 Poonen, Bjorn 29 2010 Random Diophantine equations. With appendices by Jean-Louis Colliot-Thélène and Nicholas M. Katz. Zbl 1208.11050 Poonen, Bjorn; Voloch, José Felipe 27 2004 Random polynomials having few or no real zeros. Zbl 1002.60045 Dembo, Amir; Poonen, Bjorn; Shao, Qi-Man; Zeitouni, Ofer 26 2002 Heuristics for the Brauer-Manin obstruction for curves. Zbl 1173.11040 Poonen, Bjorn 25 2006 Generalized explicit descent and its application to curves of genus 3. Zbl 1408.11065 Bruin, Nils; Poonen, Bjorn; Stoll, Michael 25 2016 Néron-Severi groups under specialization. Zbl 1248.14011 Maulik, Davesh; Poonen, Bjorn 24 2012 Mordell-Lang plus Bogomolov. Zbl 0995.11040 Poonen, Bjorn 24 1999 Gonality of modular curves in characteristic \(p\). Zbl 1138.14016 Poonen, Bjorn 24 2007 The zeta function of the beta transformation. Zbl 0843.58106 Flatto, Leopold; Lagarias, Jeffrey C.; Poonen, Bjorn 23 1994 Algebraic families of nonzero elements of Shafarevich-Tate groups. Zbl 0951.11022 Colliot-Thélène, Jean-Louis; Poonen, Bjorn 21 2000 The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields. Zbl 1294.11110 Poonen, Bjorn; Voloch, José Felipe 21 2010 Characterizing integers among rational numbers with a universal-existential formula. Zbl 1179.11047 Poonen, Bjorn 20 2009 Zeros of Fekete polynomials. Zbl 1007.11053 Conrey, Brian; Granville, Andrew; Poonen, Bjorn; Soundararajan, K. 19 2000 The moduli space of commutative algebras of finite rank. Zbl 1151.14011 Poonen, Bjorn 19 2008 Existence of rational points on smooth projective varieties. Zbl 1183.14032 Poonen, Bjorn 18 2009 Independence of points on elliptic curves arising from special points on modular and Shimura curves. II: Local results. Zbl 1232.11073 Buium, Alexandru; Poonen, Bjorn 18 2009 Lattice polygons and the number 12. Zbl 0988.52024 Poonen, Bjorn; Rodriguez-Villegas, Fernando 18 2000 Computing Néron-Severi groups and cycle class groups. Zbl 1316.14017 Poonen, Bjorn; Testa, Damiano; van Luijk, Ronald 17 2015 An explicit algebraic family of genus-one curves violating the Hasse principle. Zbl 1046.11038 Poonen, Bjorn 16 2001 The number of intersection points made by the diagonals of a regular polygon. Zbl 0913.51005 Poonen, Bjorn; Rubinstein, Michael 16 1998 Packing random intervals on-line. Zbl 0914.68082 Coffman, E. G. jun.; Flatto, L.; Jelenković, P.; Poonen, B. 16 1998 Undecidability in number theory. Zbl 1194.03018 Poonen, Bjorn 16 2008 Most odd degree hyperelliptic curves have only one rational point. Zbl 1303.11073 Poonen, Bjorn; Stoll, Michael 15 2014 Diophantine definability of infinite discrete nonarchimedean sets and Diophantine models over large subrings of number field. Zbl 1139.11056 Poonen, Bjorn; Shlapentokh, Alexandra 14 2005 Berkovich spaces embed in Euclidean spaces. Zbl 1325.14040 Hrushovski, Ehud; Loeser, François; Poonen, Bjorn 14 2014 Bertini irreducibility theorems over finite fields. Zbl 1327.14233 Charles, François; Poonen, Bjorn 14 2016 Computational aspects of curves of genus at least 2. Zbl 0891.11037 Poonen, Bjorn 13 1996 A local-global principle for densities. Zbl 1024.11047 Poonen, Bjorn; Stoll, Michael 13 1999 Some diophantine equations of the form \(x^n+y^n=z^m\). Zbl 0930.11017 Poonen, Bjorn 13 1998 On a conjecture of Helleseth regarding pairs of binary \(m\)-sequences. Zbl 0943.94513 Calderbank, A. R.; McGuire, Gary; Poonen, Bjorn; Rubinstein, Michael 12 1996 \(p\)-adic interpolation of iterates. Zbl 1291.11135 Poonen, Bjorn 12 2014 Integrality and rigidity for postcritically finite polynomials. Zbl 1291.37057 Epstein, Adam 11 2012 Computing rational points on curves. Zbl 1038.11037 Poonen, Bjorn 11 2002 Computing torsion points on curves. Zbl 1063.11017 Poonen, Bjorn 11 2001 Smooth hypersurface sections containing a given subscheme over a finite field. Zbl 1207.14047 Poonen, Bjorn 11 2008 Gonality of dynatomic curves and strong uniform boundedness of preperiodic points. Zbl 1445.37080 Doyle, John R.; Poonen, Bjorn 11 2020 Torsion in rank 1 Drinfeld modules and the uniform boundedness conjecture. Zbl 0891.11034 Poonen, Bjorn 10 1997 Convergence of the restricted Nelder-Mead algorithm in two dimensions. Zbl 1246.49029 Lagarias, Jeffrey C.; Poonen, Bjorn; Wright, Margaret H. 10 2012 Curves of every genus with many points. II: Asymptotically good families. Zbl 1072.11041 Elkies, Noam D.; Howe, Everett W.; Kresch, Andrew; Poonen, Bjorn; Wetherell, Joseph L.; Zieve, Michael E. 10 2004 Self cup products and the theta characteristic torsor. Zbl 1297.18005 Poonen, Bjorn; Rains, Eric 10 2011 Varieties without extra automorphisms. III: Hypersurfaces. Zbl 1076.14053 Poonen, Bjorn 9 2005 Undecidable problems: a sampler. Zbl 1358.03063 Poonen, Bjorn 9 2014 Varieties without extra automorphisms. II: Hyperelliptic curves. Zbl 0966.14020 Poonen, Bjorn 8 2000 The conjugate dimension of algebraic numbers. Zbl 1062.11064 Berry, Neil; Dubickas, Artūras; Elkies, Noam D.; Poonen, Bjorn; Smyth, Chris 8 2004 Abelian varieties isogenous to a power of an elliptic curve. Zbl 1400.14116 Jordan, Bruce W.; Keeton, Allan G.; Poonen, Bjorn; Rains, Eric M.; Shepherd-Barron, Nicholas; Tate, John T. 8 2018 Automorphisms of Harbater-Katz-Gabber curves. Zbl 1372.14022 Bleher, Frauke M.; Chinburg, Ted; Poonen, Bjorn; Symonds, Peter 8 2017 Varieties without extra automorphisms. I: Curves. Zbl 0966.14019 Poonen, Bjorn 7 2000 Packing random intervals. Zbl 0819.60013 Coffman, E. G. jun.; Poonen, Bjorn; Winkler, Peter 6 1995 Uniform first-order definitions in finitely generated fields. Zbl 1197.12005 Poonen, Bjorn 6 2007 A 2-adic approach to the analysis of cyclic codes. Zbl 0898.94011 Calderbank, A. R.; Li, Wen-Ching Winnie; Poonen, Bjorn 6 1997 First-order characterization of function field invariants over large fields. Zbl 1174.03015 Poonen, Bjorn; Pop, Florian 6 2008 Heuristics for the arithmetic of elliptic curves. Zbl 1443.11100 Poonen, Bjorn 6 2018 Parking arcs on the circle with applications to one-dimensional communication networks. Zbl 0812.60090 Coffman, E. G. jun.; Mallows, C. L.; Poonen, Bjorn 5 1994 Explicit methods in number theory. Rational points and Diophantine equations. Zbl 1267.11002 Belabas, Karim; Beukers, Frits; Gaudry, Pierrick; McCallum, William; Poonen, Bjorn; Siksek, Samir; Stoll, Michael; Watkins, Mark 5 2012 The set of nonsquares in a number field is diophantine. Zbl 1183.14031 Poonen, Bjorn 5 2009 Independence of points on elliptic curves arising from special points on modular and Shimura curves. I: Global results. Zbl 1177.11050 Buium, Alexandru; Poonen, Bjorn 5 2009 Curves over every global field violating the local-global principle. Zbl 1294.11108 Poonen, B. 5 2010 Using zeta functions to factor polynomials over finite fields. Zbl 1468.11247 Poonen, Bjorn 4 2019 Drinfeld modules with no supersingular primes. Zbl 0898.11024 Poonen, Bjorn 4 1998 Improved lower bounds for Shellsort. Zbl 0977.68532 Plaxton, C. Greg; Poonen, Bjorn; Suel, Torsten 4 1992 Automorphisms mapping a point into a subvariety. Zbl 1229.14032 Poonen, Bjorn 4 2011 Orbits of automorphism groups of fields. Zbl 1132.12002 Kedlaya, Kiran S.; Poonen, Bjorn 4 2005 The worst case in shellsort and related algorithms. Zbl 0784.68044 Poonen, Bjorn 4 1993 Extending self-maps to projective space over finite fields. Zbl 1303.14014 Poonen, Bjorn 4 2013 Torsion packets on curves. Zbl 0987.14020 Baker, Matthew; Poonen, Bjorn 4 2001 Arithmetic geometry, number theory, and computation. Zbl 1515.11004 4 2021 The exceptional locus in the Bertini irreducibility theorem for a morphism. Zbl 1483.14097 Poonen, Bjorn; Slavov, Kaloyan 4 2022 Average rank of elliptic curves [after Manjul Bhargava and Arul Shankar]. Zbl 1295.11065 Poonen, Bjorn 4 2013 Zeros of sparse polynomials over local fields of characteristic \(p\). Zbl 0931.11053 Poonen, Bjorn 3 1998 Fractional power series and pairings on Drinfeld modules. Zbl 0861.13010 Poonen, Bjorn 3 1996 The Hasse principle for complete intersections in projective space. Zbl 1079.14027 Poonen, Bjorn 3 2001 Multivariable polynomial injections on rational numbers. Zbl 1261.11030 Poonen, Bjorn 3 2010 Unramified covers of Galois covers of low genus curves. Zbl 1082.14035 Poonen, Bjorn 3 2005 Periodicity of a combinatorial sequence. Zbl 0644.10012 Poonen, Bjorn 3 1988 Points having the same residue field as their image under a morphism. Zbl 1077.14505 Poonen, Bjorn 3 2001 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 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 0895.11027 Howe, Everett W.; Leprévost, Franck; Poonen, Bjorn 2 1996 The exceptional locus in the Bertini irreducibility theorem for a morphism. Zbl 1483.14097 Poonen, Bjorn; Slavov, Kaloyan 4 2022 The proportion of derangements characterizes the symmetric and alternating groups. Zbl 1522.20021 Poonen, Bjorn; Slavov, Kaloyan 1 2022 The local-global principle for integral points on stacky curves. Zbl 1505.14056 Bhargava, Manjul; Poonen, Bjorn 1 2022 Arithmetic geometry, number theory, and computation. Zbl 1515.11004 4 2021 A \(p\)-adic approach to rational points on curves. Zbl 1461.11099 Poonen, Bjorn 1 2021 Gonality of dynatomic curves and strong uniform boundedness of preperiodic points. Zbl 1445.37080 Doyle, John R.; Poonen, Bjorn 11 2020 The analytic class number formula for 1-dimensional affine schemes. Zbl 1473.11212 Jordan, Bruce W.; Poonen, Bjorn 2 2020 A heuristic for boundedness of ranks of elliptic curves. Zbl 1469.11173 Park, Jennifer; Poonen, Bjorn; Voight, John; Wood, Melanie Matchett 37 2019 Using zeta functions to factor polynomials over finite fields. Zbl 1468.11247 Poonen, Bjorn 4 2019 Why all rings should have a 1. Zbl 1434.16001 Poonen, Bjorn 1 2019 A computable functor from graphs to fields. Zbl 1447.03005 Miller, Russell; Poonen, Bjorn; Schoutens, Hans; Shlapentokh, Alexandra 40 2018 Abelian varieties isogenous to a power of an elliptic curve. Zbl 1400.14116 Jordan, Bruce W.; Keeton, Allan G.; Poonen, Bjorn; Rains, Eric M.; Shepherd-Barron, Nicholas; Tate, John T. 8 2018 Heuristics for the arithmetic of elliptic curves. Zbl 1443.11100 Poonen, Bjorn 6 2018 Local arboreal representations. Zbl 1452.11140 Anderson, Jacqueline; Hamblen, Spencer; Poonen, Bjorn; Walton, Laura 2 2018 Machine-assisted proofs. Zbl 1452.68262 Davenport, James; Poonen, Bjorn; Maynard, James; Helfgott, Harald; Tiep, Pham Huu; Cruz-Filipe, Luís 2 2018 Rational points on varieties. Zbl 1387.14004 Poonen, Bjorn 101 2017 Automorphisms of Harbater-Katz-Gabber curves. Zbl 1372.14022 Bleher, Frauke M.; Chinburg, Ted; Poonen, Bjorn; Symonds, Peter 8 2017 Generalized explicit descent and its application to curves of genus 3. Zbl 1408.11065 Bruin, Nils; Poonen, Bjorn; Stoll, Michael 25 2016 Bertini irreducibility theorems over finite fields. Zbl 1327.14233 Charles, François; Poonen, Bjorn 14 2016 Galois points on varieties. Zbl 1425.11132 Jarden, Moshe; Poonen, Bjorn 1 2016 Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves. Zbl 1329.14071 Bhargava, Manjul; Kane, Daniel M.; Lenstra, Hendrik W. jun.; Poonen, Bjorn; Rains, Eric 32 2015 Computing Néron-Severi groups and cycle class groups. Zbl 1316.14017 Poonen, Bjorn; Testa, Damiano; van Luijk, Ronald 17 2015 Most odd degree hyperelliptic curves have only one rational point. Zbl 1303.11073 Poonen, Bjorn; Stoll, Michael 15 2014 Berkovich spaces embed in Euclidean spaces. Zbl 1325.14040 Hrushovski, Ehud; Loeser, François; Poonen, Bjorn 14 2014 \(p\)-adic interpolation of iterates. Zbl 1291.11135 Poonen, Bjorn 12 2014 Undecidable problems: a sampler. Zbl 1358.03063 Poonen, Bjorn 9 2014 Extending self-maps to projective space over finite fields. Zbl 1303.14014 Poonen, Bjorn 4 2013 Average rank of elliptic curves [after Manjul Bhargava and Arul Shankar]. Zbl 1295.11065 Poonen, Bjorn 4 2013 The method of Chabauty and Coleman. Zbl 1377.11077 McCallum, William; Poonen, Bjorn 53 2012 Random maximal isotropic subspaces and Selmer groups. Zbl 1294.11097 Poonen, Bjorn; Rains, Eric 43 2012 Néron-Severi groups under specialization. Zbl 1248.14011 Maulik, Davesh; Poonen, Bjorn 24 2012 Integrality and rigidity for postcritically finite polynomials. Zbl 1291.37057 Epstein, Adam 11 2012 Convergence of the restricted Nelder-Mead algorithm in two dimensions. Zbl 1246.49029 Lagarias, Jeffrey C.; Poonen, Bjorn; Wright, Margaret H. 10 2012 Explicit methods in number theory. Rational points and Diophantine equations. Zbl 1267.11002 Belabas, Karim; Beukers, Frits; Gaudry, Pierrick; McCallum, William; Poonen, Bjorn; Siksek, Samir; Stoll, Michael; Watkins, Mark 5 2012 Self cup products and the theta characteristic torsor. Zbl 1297.18005 Poonen, Bjorn; Rains, Eric 10 2011 Automorphisms mapping a point into a subvariety. Zbl 1229.14032 Poonen, Bjorn 4 2011 Insufficiency of the Brauer-Manin obstruction applied to étale covers. Zbl 1284.11096 Poonen, Bjorn 29 2010 The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields. Zbl 1294.11110 Poonen, Bjorn; Voloch, José Felipe 21 2010 Curves over every global field violating the local-global principle. Zbl 1294.11108 Poonen, B. 5 2010 Multivariable polynomial injections on rational numbers. Zbl 1261.11030 Poonen, Bjorn 3 2010 Characterizing integers among rational numbers with a universal-existential formula. Zbl 1179.11047 Poonen, Bjorn 20 2009 Existence of rational points on smooth projective varieties. Zbl 1183.14032 Poonen, Bjorn 18 2009 Independence of points on elliptic curves arising from special points on modular and Shimura curves. II: Local results. Zbl 1232.11073 Buium, Alexandru; Poonen, Bjorn 18 2009 The set of nonsquares in a number field is diophantine. Zbl 1183.14031 Poonen, Bjorn 5 2009 Independence of points on elliptic curves arising from special points on modular and Shimura curves. I: Global results. Zbl 1177.11050 Buium, Alexandru; Poonen, Bjorn 5 2009 Isomorphism types of commutative algebras of finite rank over an algebraic closed field. Zbl 1155.13015 Poonen, Bjorn 40 2008 The moduli space of commutative algebras of finite rank. Zbl 1151.14011 Poonen, Bjorn 19 2008 Undecidability in number theory. Zbl 1194.03018 Poonen, Bjorn 16 2008 Smooth hypersurface sections containing a given subscheme over a finite field. Zbl 1207.14047 Poonen, Bjorn 11 2008 First-order characterization of function field invariants over large fields. Zbl 1174.03015 Poonen, Bjorn; Pop, Florian 6 2008 Elliptic curves. Zbl 1214.11073 Poonen, Bjorn 2 2008 Twists of \(X(7)\) and primitive solutions to \(x^2+y^3=z^7\). Zbl 1124.11019 Poonen, Bjorn; Schaefer, Edward F.; Stoll, Michael 43 2007 Gonality of modular curves in characteristic \(p\). Zbl 1138.14016 Poonen, Bjorn 24 2007 Uniform first-order definitions in finitely generated fields. Zbl 1197.12005 Poonen, Bjorn 6 2007 Sieve methods for varieties over finite fields and arithmetic schemes. Zbl 1149.11031 Poonen, Bjorn 1 2007 Heuristics for the Brauer-Manin obstruction for curves. Zbl 1173.11040 Poonen, Bjorn 25 2006 Bertini theorems over finite fields. Zbl 1084.14026 Poonen, Bjorn 84 2005 Finiteness results for modular curves of genus at least 2. Zbl 1127.11041 Baker, Matthew H.; González-Jiménez, Enrique; Gonzáles, Josep; Poonen, Bjorn 36 2005 Diophantine definability of infinite discrete nonarchimedean sets and Diophantine models over large subrings of number field. Zbl 1139.11056 Poonen, Bjorn; Shlapentokh, Alexandra 14 2005 Varieties without extra automorphisms. III: Hypersurfaces. Zbl 1076.14053 Poonen, Bjorn 9 2005 Orbits of automorphism groups of fields. Zbl 1132.12002 Kedlaya, Kiran S.; Poonen, Bjorn 4 2005 Unramified covers of Galois covers of low genus curves. Zbl 1082.14035 Poonen, Bjorn 3 2005 Multiples of subvarieties in algebraic groups over finite fields. Zbl 1082.14028 Poonen, Bjorn 2 2005 Random Diophantine equations. With appendices by Jean-Louis Colliot-Thélène and Nicholas M. Katz. Zbl 1208.11050 Poonen, Bjorn; Voloch, José Felipe 27 2004 Curves of every genus with many points. II: Asymptotically good families. Zbl 1072.11041 Elkies, Noam D.; Howe, Everett W.; Kresch, Andrew; Poonen, Bjorn; Wetherell, Joseph L.; Zieve, Michael E. 10 2004 The conjugate dimension of algebraic numbers. Zbl 1062.11064 Berry, Neil; Dubickas, Artūras; Elkies, Noam D.; Poonen, Bjorn; Smyth, Chris 8 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 1047.11021 Poonen, Bjorn 53 2003 Hilbert’s Tenth Problem and Mazur’s Conjecture for large subrings of \(\mathbb{Q}\). Zbl 1028.11077 Poonen, Bjorn 30 2003 Using elliptic curves of rank one towards the undecidability of Hilbert’s tenth problem over rings of algebraic integers. Zbl 1057.11068 Poonen, Bjorn 31 2002 The Grothendieck ring of varieties is not a domain. Zbl 1054.14505 Poonen, Bjorn 29 2002 Random polynomials having few or no real zeros. Zbl 1002.60045 Dembo, Amir; Poonen, Bjorn; Shao, Qi-Man; Zeitouni, Ofer 26 2002 Computing rational points on curves. Zbl 1038.11037 Poonen, Bjorn 11 2002 The William Lowell Putnam mathematical competition 1985–2000. Problems, solutions, and commentary. Zbl 1005.00003 Kedlaya, Kiran S.; Poonen, Bjorn; Vakil, Ravi 1 2002 An explicit algebraic family of genus-one curves violating the Hasse principle. Zbl 1046.11038 Poonen, Bjorn 16 2001 Computing torsion points on curves. Zbl 1063.11017 Poonen, Bjorn 11 2001 Torsion packets on curves. Zbl 0987.14020 Baker, Matthew; Poonen, Bjorn 4 2001 The Hasse principle for complete intersections in projective space. Zbl 1079.14027 Poonen, Bjorn 3 2001 Points having the same residue field as their image under a morphism. Zbl 1077.14505 Poonen, Bjorn 3 2001 Spans of Hecke points on modular curves. Zbl 1081.11043 Poonen, Bjorn 2 2001 Large torsion subgroups of split Jacobians of curves of genus two or three. Zbl 0983.11037 Howe, Everett W.; Leprévost, Franck; Poonen, Bjorn 50 2000 Algebraic families of nonzero elements of Shafarevich-Tate groups. Zbl 0951.11022 Colliot-Thélène, Jean-Louis; Poonen, Bjorn 21 2000 Zeros of Fekete polynomials. Zbl 1007.11053 Conrey, Brian; Granville, Andrew; Poonen, Bjorn; Soundararajan, K. 19 2000 Lattice polygons and the number 12. Zbl 0988.52024 Poonen, Bjorn; Rodriguez-Villegas, Fernando 18 2000 Varieties without extra automorphisms. II: Hyperelliptic curves. Zbl 0966.14020 Poonen, Bjorn 8 2000 Varieties without extra automorphisms. I: Curves. Zbl 0966.14019 Poonen, Bjorn 7 2000 Genus-two curves with 22 torsion points. Zbl 0966.11026 Poonen, Bjorn 2 2000 The Cassels-Tate pairing on polarized Abelian varieties. Zbl 1024.11040 Poonen, Bjorn; Stoll, Michael 84 1999 Mordell-Lang plus Bogomolov. Zbl 0995.11040 Poonen, Bjorn 24 1999 A local-global principle for densities. Zbl 1024.11047 Poonen, Bjorn; Stoll, Michael 13 1999 Computing call admission capacities in linear networks. Zbl 0969.90025 Coffman, 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 0902.11025 Poonen, Bjorn 49 1998 The number of intersection points made by the diagonals of a regular polygon. Zbl 0913.51005 Poonen, Bjorn; Rubinstein, Michael 16 1998 Packing random intervals on-line. Zbl 0914.68082 Coffman, E. G. jun.; Flatto, L.; Jelenković, P.; Poonen, B. 16 1998 Some diophantine equations of the form \(x^n+y^n=z^m\). Zbl 0930.11017 Poonen, Bjorn 13 1998 Drinfeld modules with no supersingular primes. Zbl 0898.11024 Poonen, Bjorn 4 1998 Zeros of sparse polynomials over local fields of characteristic \(p\). Zbl 0931.11053 Poonen, Bjorn 3 1998 Cycles of quadratic polynomials and rational points on a genus-2 curve. Zbl 0958.11024 Flynn, E. V.; Poonen, Bjorn; Schaefer, Edward F. 60 1997 Explicit descent for Jacobians of cyclic covers of the projective line. Zbl 0888.11023 Poonen, Bjorn; Schaefer, Edward F. 51 1997 Torsion in rank 1 Drinfeld modules and the uniform boundedness conjecture. Zbl 0891.11034 Poonen, Bjorn 10 1997 ...and 15 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,646 Authors 38 Poonen, Bjorn 21 Stoll, Michael 18 Shlapentokh, Alexandra 16 Miller, Russell G. 15 Creutz, Brendan 14 Fisher, Tom A. 13 Viray, Bianca 13 Voloch, José Felipe 12 Pasten, Hector V. 11 Balakrishnan, Jennifer S. 11 Bhargava, Manjul 11 Doyle, John R. 11 Flynn, Eugene Victor 11 Ghioca, Dragos 11 Kedlaya, Kiran Sridhara 11 Loughran, Daniel 11 Wood, Melanie Matchett 10 Bazhenov, Nikolaĭ Alekseevich 10 Buium, Alexandru 10 Erdélyi, Tamás 9 Howe, Everett W. 9 Lorenzo García, Elisa 9 Siksek, Samir 8 Cornelissen, Gunther 8 Gonzalez Rovira, Josep 8 Mazur, Barry 8 Ritzenthaler, Christophe 8 Silverman, Joseph Hillel 7 Asgarli, Shamil 7 Borwein, Peter Benjamin 7 Browning, Timothy Daniel 7 Bruin, Nils 7 Harrison-Trainor, Matthew 7 Ishitsuka, Yasuhiro 7 Katz, Daniel J. 7 Krumm, David 7 Li, Wanlin 7 Liu, Qing 7 Müller, Jan Steffen 7 Nakahara, Masahiro 7 Rojas, J. Maurice 7 Shparlinski, Igor E. 7 Tanimoto, Sho 7 Várilly-Alvarado, Anthony 7 Zureick-Brown, David 6 Cao, Yang 6 Colliot-Thélène, Jean-Louis 6 Cremona, John E. 6 Fehm, Arno 6 Freitas, Nuno 6 Ingram, Patrick 6 Liang, Yongqi 6 Melnikov, Alexander G. 6 Schaefer, Edward F. 6 Voight, John Michael 5 Bars Cortina, Francesc 5 Bennett, Michael A. 5 Berenhaut, Kenneth S. 5 Dujella, Andrej 5 Elias, Joan 5 Faber, Xander 5 Hashimoto, Sachi 5 Hindes, Wade 5 Hirakawa, Yoshinosuke 5 Ito, Tetsushi 5 Knight, Julia F. 5 Langevin, Philippe 5 Lorenzini, Dino J. 5 Manes, Michelle 5 Micheli, Giacomo 5 Pries, Rachel J. 5 Ray, Anwesh 5 Rubin, Karl Cooper 5 Sadek, Mohammad 5 Sijsling, Jeroen 5 Sutherland, Andrew V. 5 Wang, Xiaoheng 5 Wu, Han 5 Xue, Jiangwei 5 Zarkhin, Yuriĭ Gennad’evich 4 Baryshnikov, Yuliy M. 4 Benedetto, Robert L. 4 Bianchi, Francesca 4 Bruhn, Henning 4 Casnati, Gianfranco 4 Castryck, Wouter 4 Česnavičius, Kęstutis 4 Clark, Peter Louis 4 David, Chantal 4 de Graaf, Willem Adriaan 4 Dembo, Amir 4 Dokchitser, Vladimir 4 Favre, Charles 4 Finotti, Luís R. A. 4 González-Jiménez, Enrique 4 Habegger, Philipp 4 Hare, Kevin G. 4 Harpaz, Yonatan 4 Ho, Wei 4 Homs Pons, Roser ...and 1,546 more Authors all top 5 Cited in 274 Serials 109 Journal of Number Theory 52 Mathematics of Computation 50 Transactions of the American Mathematical Society 46 Journal de Théorie des Nombres de Bordeaux 42 Advances in Mathematics 42 Journal of Algebra 40 International Journal of Number Theory 36 Compositio Mathematica 33 Mathematische Annalen 33 Proceedings of the American Mathematical Society 31 Research in Number Theory 30 Duke Mathematical Journal 25 Journal of Pure and Applied Algebra 24 Algebra & Number Theory 20 Manuscripta Mathematica 19 Mathematical Proceedings of the Cambridge Philosophical Society 19 Acta Arithmetica 19 Mathematische Zeitschrift 18 Inventiones Mathematicae 18 Annals of Mathematics. 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Commentarii Mathematici 4 European Journal of Combinatorics 4 Ergodic Theory and Dynamical Systems 4 Discrete & Computational Geometry 4 Revista Matemática Iberoamericana 4 SIAM Journal on Discrete Mathematics 4 Designs, Codes and Cryptography 4 Stochastic Processes and their Applications 4 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 4 The New York Journal of Mathematics 4 Acta Mathematica Sinica. English Series 4 Journal of the Australian Mathematical Society 4 Forum of Mathematics, Pi 3 Communications in Mathematical Physics 3 Indian Journal of Pure & Applied Mathematics 3 Journal d’Analyse Mathématique 3 American Journal of Mathematics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Canadian Mathematical Bulletin 3 Illinois Journal of Mathematics 3 Probability Theory and Related Fields 3 International Journal of Mathematics 3 International Journal of Algebra and Computation 3 IMRN. International Mathematics Research Notices 3 The Journal of Geometric Analysis 3 Expositiones Mathematicae 3 Archive for Mathematical Logic 3 Applicable Algebra in Engineering, Communication and Computing 3 Journal of Algebraic Combinatorics ...and 174 more Serials all top 5 Cited in 54 Fields 960 Number theory (11-XX) 784 Algebraic geometry (14-XX) 105 Mathematical logic and foundations (03-XX) 104 Dynamical systems and ergodic theory (37-XX) 84 Field theory and polynomials (12-XX) 80 Combinatorics (05-XX) 79 Commutative algebra (13-XX) 71 Probability theory and stochastic processes (60-XX) 63 Group theory and generalizations (20-XX) 45 Functions of a complex variable (30-XX) 41 Computer science (68-XX) 33 Information and communication theory, circuits (94-XX) 29 Several complex variables and analytic spaces (32-XX) 26 Linear and multilinear algebra; matrix theory (15-XX) 25 Real functions (26-XX) 23 Associative rings and algebras (16-XX) 20 Convex and discrete geometry (52-XX) 18 \(K\)-theory (19-XX) 18 Operations research, mathematical programming (90-XX) 17 Order, lattices, ordered algebraic structures (06-XX) 17 Algebraic topology (55-XX) 14 Nonassociative rings and algebras (17-XX) 14 Numerical analysis (65-XX) 13 Geometry (51-XX) 11 Manifolds and cell complexes (57-XX) 11 Quantum theory (81-XX) 10 Category theory; homological algebra (18-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 10 Differential geometry (53-XX) 8 General and overarching topics; collections (00-XX) 8 History and biography (01-XX) 8 Topological groups, Lie groups (22-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 Functional analysis (46-XX) 6 Measure and integration (28-XX) 5 Special functions (33-XX) 5 Partial differential equations (35-XX) 5 Approximations and expansions (41-XX) 3 General algebraic systems (08-XX) 3 Statistics (62-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 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Ordinary differential equations (34-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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