Edit Profile (opens in new tab) Lipshitz, Leonard Co-Author Distance Author ID: lipshitz.leonard Published as: Lipshitz, L.; Lipshitz, Leonard Further Spellings: Lipshitz, Leonard Michael Homepage: https://www.math.purdue.edu/people/bio/lipshitz/home External Links: MGP · dblp · GND Documents Indexed: 45 Publications since 1973, including 1 Book 1 Contribution as Editor Co-Authors: 10 Co-Authors with 31 Joint Publications 292 Co-Co-Authors all top 5 Co-Authors 14 single-authored 10 Robinson, Zachary 9 Denef, Jan 6 Becker, Joseph A. 4 Cluckers, Raf 4 Rubel, Lee Albert 2 Pheidas, Thanases 1 Nadel, Mark E. 1 van den Dries, Lou 1 van der Poorten, Alfred J. 1 Van Geel, Jan all top 5 Serials 7 Proceedings of the American Mathematical Society 6 Transactions of the American Mathematical Society 3 American Journal of Mathematics 3 Fundamenta Mathematicae 3 Journal of the London Mathematical Society. Second Series 3 The Journal of Symbolic Logic 2 Journal of Algebra 2 Journal für die Reine und Angewandte Mathematik 2 Mathematische Annalen 2 Journal of the European Mathematical Society (JEMS) 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Bulletin of the London Mathematical Society 1 Canadian Journal of Mathematics 1 Inventiones Mathematicae 1 Journal of Number Theory 1 Proceedings of the London Mathematical Society. Third Series 1 Bulletin de la Société Matheḿatique de Belgique. Série B 1 Astérisque 1 Contemporary Mathematics all top 5 Fields 30 Mathematical logic and foundations (03-XX) 14 Field theory and polynomials (12-XX) 14 Several complex variables and analytic spaces (32-XX) 13 Commutative algebra (13-XX) 13 Algebraic geometry (14-XX) 12 Number theory (11-XX) 5 Ordinary differential equations (34-XX) 5 Computer science (68-XX) 2 Functions of a complex variable (30-XX) 2 Numerical analysis (65-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Geometry (51-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 41 Publications have been cited 604 times in 426 Documents Cited by ▼ Year ▼ D-finite power series. Zbl 0695.12018Lipshitz, L. 68 1989 The diagonal of a D-finite power series is D-finite. Zbl 0657.13024Lipshitz, L. 55 1988 Power series solutions of algebraic differential equations. Zbl 0518.12015Denef, J.; Lipshitz, L. 38 1984 Diophantine sets over some rings of algebraic integers. Zbl 0399.10049Denef, J.; Lipshitz, L. 37 1978 Algebraic power series and diagonals. Zbl 0609.12020Denef, J.; Lipshitz, L. 34 1987 Ultraproducts and approximation in local rings. I. Zbl 0416.13004Becker, Joseph; Denef, J.; Lipshitz, L.; Van den Dries, Lou 32 1979 Fields with analytic structure. Zbl 1291.03074Cluckers, R.; Lipshitz, L. 31 2011 Rigid subanalytic sets. Zbl 0792.14010Lipshitz, L. 28 1993 The Diophantine problem for addition and divisibility. Zbl 0374.02025Lipshitz, L. 27 1978 Analytic cell decomposition and analytic motivic integration. Zbl 1168.12006Cluckers, Raf; Lipshitz, Leonard; Robinson, Zachary 22 2006 The model companion of the theory of commutative rings without nilpotent elements. Zbl 0267.02040Lipshitz, L.; Saracino, D. 20 1973 Ultraproducts and approximation in local rings. II. Zbl 0426.13010Denef, J.; Lipshitz, L. 19 1980 A differentially algebraic replacement theorem, and analog computability. Zbl 0626.34012Lipshitz, Leonard; Rubel, Lee A. 15 1987 One-dimensional fibers of rigid subanalytic sets. Zbl 0903.32004Lipshitz, L.; Robinson, Z. 14 1998 Rings of separated power series and quasi-affinoid geometry. Zbl 0957.32011Lipshitz, Leonard; Robinson, Zachary 14 2000 Strictly convergent analytic structures. Zbl 1372.32031Cluckers, Raf; Lipshitz, Leonard 13 2017 A gap theorem for power series solutions of algebraic differential equations. Zbl 0605.12014Lipshitz, Leonard; Rubel, Lee A. 13 1986 Decision problems for differential equations. Zbl 0683.03039Denef, J.; Lipshitz, L. 11 1989 An analogue of Hilbert’s tenth problem for \(p\)-adic entire functions. Zbl 0849.03007Lipshitz, Leonard; Pheidas, Thanases 9 1995 Uniform properties of rigid subanalytic sets. Zbl 1081.03024Lipshitz, Leonard; Robinson, Zachary 9 2005 Hilbert’s tenth problem: relations with arithmetic and algebraic geometry. Proceedings of the workshop, Ghent University, Belgium, November 2–5, 1999. Zbl 0955.00034 9 2000 The undecidability of the word problems for projective geometries and modular lattices. Zbl 0288.02026Lipshitz, L. 9 1974 Remarks of the elementary theories of formal and convergent power series. Zbl 0526.13016Becker, Joseph; Lipshitz, Leonard 7 1980 Rigid subanalytic subsets of the line and the plane. Zbl 0935.14035Lipshitz, Leonard; Robinson, Zachary 7 1996 Overconvergent real closed quantifier elimination. Zbl 1116.03032Lipshitz, L.; Robinson, Z. 7 2006 Further remarks on the elementary theory of formal power series rings. Zbl 0452.12013Becker, J.; Denef, J.; Lipshitz, L. 6 1980 Isolated points on fibers of affinoid varieties. Zbl 0636.14006Lipshitz, L. 6 1988 Rigid subanalytic subsets of curves and surfaces. Zbl 0935.32008Lipshitz, Leonard; Robinson, Zachary 5 1999 Undecidable existential problems for addition and divisibility in algebraic number rings. II. Zbl 0365.02019Lipshitz, Leonard 5 1977 Undecidable existential problems for addition and divisibility in algebraic number rings. Zbl 0385.03012Lipshitz, L. 5 1978 Dimension theory and smooth stratification of rigid subanalytic sets. Zbl 0978.14046Lipshitz, Leonard; Robinson, Zachary 5 2000 Some remarks on the diophantive problem for addition and divisibility. Zbl 0497.03007Lipshitz, Leonard 4 1981 Real closed fields with non-standard and standard analytic structure. Zbl 1184.03032Cluckers, R.; Lipshitz, L.; Robinson, Z. 4 2008 The approximation property for some 5-dimensional Henselian rings. Zbl 0531.14004Becker, Joseph; Denef, J.; Lipshitz, L. 3 1983 Commutative regular rings with integral closure. Zbl 0315.13006Lipshitz, L. 3 1975 The real closure of a commutative regular \(f\)-ring. Zbl 0359.02057Lipshitz, L. 3 1977 Corrigendum to: “A differentially algebraic replacement theorem, and analog computability”. Zbl 0691.34010Lipshitz, Leonard; Rubel, Lee A. 2 1988 Rational functions, diagonals, automata and arithmetic. Zbl 0694.10008Lipshitz, Leonard; van der Poorten, Alfred J. 2 1990 Flattening and analytic continuation of affinoid morphisms: remarks on a paper of Gardener and Schoutens. Zbl 1080.32020Lipshitz, L.; Robinson, Z. 1 2005 The additive structure of models of arithmetic. Zbl 0383.03047Lipshitz, Leonard; Nadel, Mark 1 1978 p-adic zeros of polynomials. Zbl 0653.12006Lipshitz, L. 1 1988 Strictly convergent analytic structures. Zbl 1372.32031Cluckers, Raf; Lipshitz, Leonard 13 2017 Fields with analytic structure. Zbl 1291.03074Cluckers, R.; Lipshitz, L. 31 2011 Real closed fields with non-standard and standard analytic structure. Zbl 1184.03032Cluckers, R.; Lipshitz, L.; Robinson, Z. 4 2008 Analytic cell decomposition and analytic motivic integration. Zbl 1168.12006Cluckers, Raf; Lipshitz, Leonard; Robinson, Zachary 22 2006 Overconvergent real closed quantifier elimination. Zbl 1116.03032Lipshitz, L.; Robinson, Z. 7 2006 Uniform properties of rigid subanalytic sets. Zbl 1081.03024Lipshitz, Leonard; Robinson, Zachary 9 2005 Flattening and analytic continuation of affinoid morphisms: remarks on a paper of Gardener and Schoutens. Zbl 1080.32020Lipshitz, L.; Robinson, Z. 1 2005 Rings of separated power series and quasi-affinoid geometry. Zbl 0957.32011Lipshitz, Leonard; Robinson, Zachary 14 2000 Hilbert’s tenth problem: relations with arithmetic and algebraic geometry. Proceedings of the workshop, Ghent University, Belgium, November 2–5, 1999. Zbl 0955.00034 9 2000 Dimension theory and smooth stratification of rigid subanalytic sets. Zbl 0978.14046Lipshitz, Leonard; Robinson, Zachary 5 2000 Rigid subanalytic subsets of curves and surfaces. Zbl 0935.32008Lipshitz, Leonard; Robinson, Zachary 5 1999 One-dimensional fibers of rigid subanalytic sets. Zbl 0903.32004Lipshitz, L.; Robinson, Z. 14 1998 Rigid subanalytic subsets of the line and the plane. Zbl 0935.14035Lipshitz, Leonard; Robinson, Zachary 7 1996 An analogue of Hilbert’s tenth problem for \(p\)-adic entire functions. Zbl 0849.03007Lipshitz, Leonard; Pheidas, Thanases 9 1995 Rigid subanalytic sets. Zbl 0792.14010Lipshitz, L. 28 1993 Rational functions, diagonals, automata and arithmetic. Zbl 0694.10008Lipshitz, Leonard; van der Poorten, Alfred J. 2 1990 D-finite power series. Zbl 0695.12018Lipshitz, L. 68 1989 Decision problems for differential equations. Zbl 0683.03039Denef, J.; Lipshitz, L. 11 1989 The diagonal of a D-finite power series is D-finite. Zbl 0657.13024Lipshitz, L. 55 1988 Isolated points on fibers of affinoid varieties. Zbl 0636.14006Lipshitz, L. 6 1988 Corrigendum to: “A differentially algebraic replacement theorem, and analog computability”. Zbl 0691.34010Lipshitz, Leonard; Rubel, Lee A. 2 1988 p-adic zeros of polynomials. Zbl 0653.12006Lipshitz, L. 1 1988 Algebraic power series and diagonals. Zbl 0609.12020Denef, J.; Lipshitz, L. 34 1987 A differentially algebraic replacement theorem, and analog computability. Zbl 0626.34012Lipshitz, Leonard; Rubel, Lee A. 15 1987 A gap theorem for power series solutions of algebraic differential equations. Zbl 0605.12014Lipshitz, Leonard; Rubel, Lee A. 13 1986 Power series solutions of algebraic differential equations. Zbl 0518.12015Denef, J.; Lipshitz, L. 38 1984 The approximation property for some 5-dimensional Henselian rings. Zbl 0531.14004Becker, Joseph; Denef, J.; Lipshitz, L. 3 1983 Some remarks on the diophantive problem for addition and divisibility. Zbl 0497.03007Lipshitz, Leonard 4 1981 Ultraproducts and approximation in local rings. II. Zbl 0426.13010Denef, J.; Lipshitz, L. 19 1980 Remarks of the elementary theories of formal and convergent power series. Zbl 0526.13016Becker, Joseph; Lipshitz, Leonard 7 1980 Further remarks on the elementary theory of formal power series rings. Zbl 0452.12013Becker, J.; Denef, J.; Lipshitz, L. 6 1980 Ultraproducts and approximation in local rings. I. Zbl 0416.13004Becker, Joseph; Denef, J.; Lipshitz, L.; Van den Dries, Lou 32 1979 Diophantine sets over some rings of algebraic integers. Zbl 0399.10049Denef, J.; Lipshitz, L. 37 1978 The Diophantine problem for addition and divisibility. Zbl 0374.02025Lipshitz, L. 27 1978 Undecidable existential problems for addition and divisibility in algebraic number rings. Zbl 0385.03012Lipshitz, L. 5 1978 The additive structure of models of arithmetic. Zbl 0383.03047Lipshitz, Leonard; Nadel, Mark 1 1978 Undecidable existential problems for addition and divisibility in algebraic number rings. II. Zbl 0365.02019Lipshitz, Leonard 5 1977 The real closure of a commutative regular \(f\)-ring. Zbl 0359.02057Lipshitz, L. 3 1977 Commutative regular rings with integral closure. Zbl 0315.13006Lipshitz, L. 3 1975 The undecidability of the word problems for projective geometries and modular lattices. Zbl 0288.02026Lipshitz, L. 9 1974 The model companion of the theory of commutative rings without nilpotent elements. Zbl 0267.02040Lipshitz, L.; Saracino, D. 20 1973 all cited Publications top 5 cited Publications all top 5 Cited by 393 Authors 19 Cluckers, Raf 19 Shlapentokh, Alexandra 15 Lipshitz, Leonard 14 Bousquet-Mélou, Mireille 11 Bostan, Alin 8 Halupczok, Immanuel 8 Rechnitzer, Andrew Daniel 8 van der Hoeven, Joris 7 Denef, Jan 7 Kauers, Manuel 7 Loeser, François 7 Pasten, Hector V. 7 Rond, Guillaume 7 Rubel, Lee Albert 7 van den Dries, Lou 6 Falkensteiner, Sebastian 6 Melczer, Stephen 6 Mishna, Marni 6 Pheidas, Thanases 6 Popescu, Dorin 6 Salvy, Bruno 6 Schoutens, Hans 5 Aschenbrenner, Matthias 5 Bell, Jason P. 5 Chen, Shaoshi 5 Robinson, Zachary 4 Allouche, Jean-Paul Simon 4 Costa, José Félix 4 Cubides Kovacsics, Pablo 4 Haskell, Deirdre 4 Kaiser, Tobias 4 Leĭnartas, Evgeniĭ Konstantinovich 4 Macpherson, Dugald 4 Martin, Florent 4 Myasnikov, Alexei G. 4 Paramonov, Serge V. 4 Yakovleva, Tatiana I. 4 Yurkevich, Sergey V. 3 Abramov, Sergeĭ Aleksandrovich 3 Becker, Joseph A. 3 Bournez, Olivier 3 Campagnolo, Manuel Lameiras 3 Çelikler, Y. Firat 3 Chyzak, Frédéric 3 Dang, Zhe 3 Forey, Arthur 3 Graça, Daniel Silva 3 Guttmann, Anthony John 3 Herrmann, Christian 3 Hrushovski, Ehud 3 Ibarra, Oscar H. 3 Koutschan, Christoph 3 Lyapin, Alexander Petrovich 3 Maillard, Jean-Marie 3 Mansour, Toufik 3 Martinez-Ranero, Carlos Azarel 3 Massazza, Paolo 3 Moore, Cristopher 3 Nowak, Krzysztof Jan 3 Raschel, Kilian 3 Rotthaus, Christel 3 Roush, Fred William 3 Sendra, Juan Rafael 3 Singer, Michael F. 3 Sirokofskich, Alla 3 Skordev, Gencho S. 3 Starchak, Mikhail R. 3 Sureson, Claude 3 Tucker, John V. 3 Vidaux, Xavier 3 Weispfenning, Volker 3 Wilson, Mark Curtis 3 Zeilberger, Doron 2 Abdelaziz, Y. 2 Alexandru, Victor 2 Beaton, Nicholas R. 2 Beggs, Edwin J. 2 Bélair, Luc 2 Bergeron, François 2 Bernardi, Olivier 2 Boix, Alberto Fernandez 2 Boulier, François 2 Cano, José Maria 2 Cerda-Romero, Leonidas 2 Comte, Georges 2 Cornelissen, Gunther 2 Courtiel, Julien 2 Delon, Françoise 2 Drmota, Michael 2 Edmundo, Mário J. 2 Garay López, Cristhian 2 Garcia-Fritz, Natalia 2 Garreta, Albert 2 Gessel, Ira Martin 2 Gordon, Julia 2 Hainry, Emmanuel 2 Hauser, Herwig 2 Johnson, Will 2 Kartas, Konstantinos 2 Kerner, Dmitry ...and 293 more Authors all top 5 Cited in 124 Serials 25 Journal of Algebra 23 Transactions of the American Mathematical Society 17 The Journal of Symbolic Logic 17 Proceedings of the American Mathematical Society 16 Theoretical Computer Science 16 Journal of Symbolic Computation 14 Journal of Combinatorial Theory. Series A 14 Annals of Pure and Applied Logic 12 Israel Journal of Mathematics 10 Journal of Number Theory 9 Advances in Applied Mathematics 7 Inventiones Mathematicae 7 Mathematische Annalen 7 Mathematische Zeitschrift 7 Archive for Mathematical Logic 6 Manuscripta Mathematica 5 Advances in Mathematics 5 Duke Mathematical Journal 5 Journal für die Reine und Angewandte Mathematik 5 Programming and Computer Software 5 Journal of Complexity 5 Selecta Mathematica. New Series 5 Algebra & Number Theory 4 Algebra Universalis 4 Compositio Mathematica 4 Journal of Pure and Applied Algebra 4 European Journal of Combinatorics 4 Journal de Théorie des Nombres de Bordeaux 4 Journal of the European Mathematical Society (JEMS) 4 Foundations of Computational Mathematics 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 International Journal of Number Theory 3 Communications in Algebra 3 Discrete Mathematics 3 Journal of Differential Equations 3 Vestnik St. Petersburg University. Mathematics 3 Mathematical Logic Quarterly (MLQ) 3 Annals of Combinatorics 3 Journal of the Institute of Mathematics of Jussieu 3 Mathematics in Computer Science 3 Journal of Physics A: Mathematical and Theoretical 3 Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika 3 Journal of Siberian Federal University. Mathematics & Physics 2 Bulletin of the Australian Mathematical Society 2 Annales de l’Institut Fourier 2 Journal of Soviet Mathematics 2 Mathematische Nachrichten 2 Discrete & Computational Geometry 2 Journal of the American Mathematical Society 2 SIAM Journal on Discrete Mathematics 2 International Journal of Algebra and Computation 2 Bulletin of the American Mathematical Society. New Series 2 Journal of Algebraic Combinatorics 2 Journal of Mathematical Sciences (New York) 2 The Electronic Journal of Combinatorics 2 Séminaire Lotharingien de Combinatoire 2 Forum of Mathematics, Pi 2 Transactions of the American Mathematical Society. Series B 1 Communications in Mathematical Physics 1 Discrete Applied Mathematics 1 Information Processing Letters 1 Rocky Mountain Journal of Mathematics 1 Mathematics of Computation 1 Algebra and Logic 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Applied Mathematics and Computation 1 Glasgow Mathematical Journal 1 Information Sciences 1 Journal of Computational and Applied Mathematics 1 Journal of Computer and System Sciences 1 Journal of the Mathematical Society of Japan 1 Mathematics and Computers in Simulation 1 Monatshefte für Mathematik 1 Nagoya Mathematical Journal 1 Notre Dame Journal of Formal Logic 1 Osaka Journal of Mathematics 1 Pacific Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Proceedings of the London Mathematical Society. Third Series 1 Rendiconti del Seminario Matematico della Università di Padova 1 Siberian Mathematical Journal 1 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 1 Cybernetics 1 Algorithmica 1 Information and Computation 1 International Journal of Mathematics 1 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série 1 The Annals of Applied Probability 1 Geometric and Functional Analysis. GAFA 1 RAIRO. Informatique Théorique et Applications 1 Applicable Algebra in Engineering, Communication and Computing 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Combinatorics, Probability and Computing 1 Annales Mathématiques Blaise Pascal 1 The Bulletin of Symbolic Logic 1 Integral Transforms and Special Functions 1 Annals of Mathematics and Artificial Intelligence 1 Journal of Difference Equations and Applications 1 Izvestiya: Mathematics 1 Algebras and Representation Theory ...and 24 more Serials all top 5 Cited in 41 Fields 173 Mathematical logic and foundations (03-XX) 118 Number theory (11-XX) 92 Algebraic geometry (14-XX) 86 Field theory and polynomials (12-XX) 80 Commutative algebra (13-XX) 64 Computer science (68-XX) 61 Combinatorics (05-XX) 40 Several complex variables and analytic spaces (32-XX) 28 Ordinary differential equations (34-XX) 21 Special functions (33-XX) 18 Associative rings and algebras (16-XX) 14 Group theory and generalizations (20-XX) 14 Functions of a complex variable (30-XX) 12 Order, lattices, ordered algebraic structures (06-XX) 12 Difference and functional equations (39-XX) 8 Partial differential equations (35-XX) 7 Category theory; homological algebra (18-XX) 7 Real functions (26-XX) 6 Numerical analysis (65-XX) 5 Convex and discrete geometry (52-XX) 5 Probability theory and stochastic processes (60-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Sequences, series, summability (40-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 General algebraic systems (08-XX) 3 Topological groups, Lie groups (22-XX) 3 Functional analysis (46-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Approximations and expansions (41-XX) 2 Geometry (51-XX) 2 Algebraic topology (55-XX) 2 Manifolds and cell complexes (57-XX) 2 Mechanics of particles and systems (70-XX) 2 Quantum theory (81-XX) 1 General and overarching topics; collections (00-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 Operator theory (47-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year