Edit Profile (opens in new tab) Brown, Francis C. S. Co-Author Distance Author ID: brown.francis-c-s Published as: Brown, Francis; Brown, Francis C. S. External Links: MGP · Wikidata Documents Indexed: 36 Publications since 2004 Co-Authors: 12 Co-Authors with 15 Joint Publications 173 Co-Co-Authors all top 5 Co-Authors 21 single-authored 4 Schnetz, Oliver 3 Dupont, Clément 2 Yeats, Karen A. 1 Bergström, Jonas 1 Bogner, Christian 1 Carr, Sarah 1 Fink, Thomas M. A. 1 Hain, Richard M. 1 Kreimer, Dirk 1 Omar, Sami 1 Schneps, Leila 1 Willbrand, Karen all top 5 Serials 4 Communications in Number Theory and Physics 3 Communications in Mathematical Physics 3 Journal of Number Theory 3 Forum of Mathematics, Sigma 2 Compositio Mathematica 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Research in the Mathematical Sciences 1 Discrete Mathematics 1 Letters in Mathematical Physics 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Duke Mathematical Journal 1 Inventiones Mathematicae 1 Journal für die Reine und Angewandte Mathematik 1 Nagoya Mathematical Journal 1 Advances in Theoretical and Mathematical Physics 1 Annals of Mathematics. Second Series 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Algebra & Number Theory 1 Moscow Journal of Combinatorics and Number Theory all top 5 Fields 27 Number theory (11-XX) 17 Algebraic geometry (14-XX) 14 Quantum theory (81-XX) 4 Combinatorics (05-XX) 3 Associative rings and algebras (16-XX) 3 Special functions (33-XX) 2 Commutative algebra (13-XX) 2 Category theory; homological algebra (18-XX) 2 \(K\)-theory (19-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Computer science (68-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 36 Publications have been cited 869 times in 447 Documents Cited by ▼ Year ▼ Mixed Tate motives over \(\mathbb{Z}\). Zbl 1278.19008Brown, Francis 137 2012 On the decomposition of motivic multiple zeta values. Zbl 1321.11087Brown, Francis C. S. 65 2012 Single-valued motivic periods and multiple zeta values. Zbl 1377.11099Brown, Francis 64 2014 Single-valued multiple polylogarithms in one variable. (Polylogarithmes multiples uniformes en une variable.) Zbl 1048.11053Brown, Francis C. S. 62 2004 The massless higher-loop two-point function. Zbl 1196.81130Brown, Francis 56 2009 Multiple zeta values and periods of moduli spaces \(\overline{\mathfrak M}_{0,n}\). Zbl 1216.11079Brown, Francis C. S. 54 2009 A \(K3\) in \(\phi^{4}\). Zbl 1253.14024Brown, Francis; Schnetz, Oliver 49 2012 Notes on motivic periods. Zbl 1390.14024Brown, Francis 34 2017 Feynman amplitudes, coaction principle, and cosmic Galois group. Zbl 1395.81117Brown, Francis 30 2017 A class of non-holomorphic modular forms. I. Zbl 1441.11103Brown, Francis 30 2018 Angles, scales and parametric renormalization. Zbl 1273.81164Brown, Francis; Kreimer, Dirk 28 2013 Feynman integrals and iterated integrals on moduli spaces of curves of genus zero. Zbl 1316.81040Bogner, Christian; Brown, Francis 23 2015 Spanning forest polynomials and the transcendental weight of Feynman graphs. Zbl 1223.05019Brown, Francis; Yeats, Karen 23 2011 A class of nonholomorphic modular forms. II: Equivariant iterated Eisenstein integrals. Zbl 1452.11054Brown, Francis 20 2020 Modular forms in quantum field theory. Zbl 1290.81083Brown, Francis; Schnetz, Oliver 19 2013 Single-valued multiple polylogarithms and a proof of the zig-zag conjecture. Zbl 1395.11115Brown, Francis; Schnetz, Oliver 19 2015 Single-valued integration and superstring amplitudes in genus zero. Zbl 1483.81117Brown, Francis; Dupont, Clément 18 2021 Iterated integrals in quantum field theory. Zbl 1295.81072Brown, Francis 13 2013 A class of non-holomorphic modular forms. III: real analytic cusp forms for \(\mathrm{SL}_2(\mathbb{Z})\). Zbl 1440.11071Brown, Francis 13 2018 Irrationality proofs for zeta values, moduli spaces and dinner parties. Zbl 1370.11103Brown, Francis 12 2016 Zeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curve. Zbl 1422.11180Brown, Francis 12 2017 Properties of \(c_2\) invariants of Feynman graphs. Zbl 1309.81174Brown, Francis; Schnetz, Oliver; Yeats, Karen 11 2014 Depth-graded motivic multiple zeta values. Zbl 1481.11084Brown, Francis 11 2021 Li’s criterion and zero-free regions of \(L\)-functions. Zbl 1154.11334Brown, Francis C. S. 10 2005 Single-valued integration and double copy. Zbl 1484.14043Brown, Francis; Dupont, Clément 8 2021 Motivic periods and \(\mathbb{P}^1\setminus\{0,1,\infty\}\). Zbl 1373.11064Brown, Francis 8 2014 Multiple zeta values and periods of moduli spaces \(\bar {\mathfrak M}_{0,n}\). (Périodes des espaces des modules \(\bar {\mathfrak M}_{0,n}\) et valeurs zêtas multiples.) Zbl 1105.11019Brown, Francis C. S. 7 2006 Multiple zeta values and periods: from moduli spaces to Feynman integrals. Zbl 1228.81214Brown, Francis 6 2011 On arithmetic and asymptotic properties of up-down numbers. Zbl 1126.05010Brown, Francis C. S.; Fink, Thomas M. A.; Willbrand, Karen 5 2007 The algebra of cell-zeta values. Zbl 1195.14078Brown, Francis; Carr, Sarah; Schneps, Leila 5 2010 Algebraic de Rham theory for weakly holomorphic modular forms of level one. Zbl 1422.11083Brown, Francis; Hain, Richard 4 2018 Inversion of series and the cohomology of the moduli spaces \({\mathcal M}^\delta_{0,n}\). Zbl 1228.14026Bergström, Jonas; Brown, Francis 4 2010 Li’s criterion for Epstein zeta functions, generalization of Kronecker’s limit formula and the Gauss problem. Zbl 1400.11091Brown, Francis; Omar, Sami 3 2016 Dedekind zeta motives for totally real number fields. Zbl 1286.14006Brown, Francis C. S. 3 2013 Invariant differential forms on complexes of graphs and Feynman integrals. Zbl 1479.18013Brown, Francis 2 2021 Lauricella hypergeometric functions, unipotent fundamental groups of the punctured Riemann sphere, and their motivic coactions. Zbl 1516.14013Brown, Francis; Dupont, Clément 1 2023 Lauricella hypergeometric functions, unipotent fundamental groups of the punctured Riemann sphere, and their motivic coactions. Zbl 1516.14013Brown, Francis; Dupont, Clément 1 2023 Single-valued integration and superstring amplitudes in genus zero. Zbl 1483.81117Brown, Francis; Dupont, Clément 18 2021 Depth-graded motivic multiple zeta values. Zbl 1481.11084Brown, Francis 11 2021 Single-valued integration and double copy. Zbl 1484.14043Brown, Francis; Dupont, Clément 8 2021 Invariant differential forms on complexes of graphs and Feynman integrals. Zbl 1479.18013Brown, Francis 2 2021 A class of nonholomorphic modular forms. II: Equivariant iterated Eisenstein integrals. Zbl 1452.11054Brown, Francis 20 2020 A class of non-holomorphic modular forms. I. Zbl 1441.11103Brown, Francis 30 2018 A class of non-holomorphic modular forms. III: real analytic cusp forms for \(\mathrm{SL}_2(\mathbb{Z})\). Zbl 1440.11071Brown, Francis 13 2018 Algebraic de Rham theory for weakly holomorphic modular forms of level one. Zbl 1422.11083Brown, Francis; Hain, Richard 4 2018 Notes on motivic periods. Zbl 1390.14024Brown, Francis 34 2017 Feynman amplitudes, coaction principle, and cosmic Galois group. Zbl 1395.81117Brown, Francis 30 2017 Zeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curve. Zbl 1422.11180Brown, Francis 12 2017 Irrationality proofs for zeta values, moduli spaces and dinner parties. Zbl 1370.11103Brown, Francis 12 2016 Li’s criterion for Epstein zeta functions, generalization of Kronecker’s limit formula and the Gauss problem. Zbl 1400.11091Brown, Francis; Omar, Sami 3 2016 Feynman integrals and iterated integrals on moduli spaces of curves of genus zero. Zbl 1316.81040Bogner, Christian; Brown, Francis 23 2015 Single-valued multiple polylogarithms and a proof of the zig-zag conjecture. Zbl 1395.11115Brown, Francis; Schnetz, Oliver 19 2015 Single-valued motivic periods and multiple zeta values. Zbl 1377.11099Brown, Francis 64 2014 Properties of \(c_2\) invariants of Feynman graphs. Zbl 1309.81174Brown, Francis; Schnetz, Oliver; Yeats, Karen 11 2014 Motivic periods and \(\mathbb{P}^1\setminus\{0,1,\infty\}\). Zbl 1373.11064Brown, Francis 8 2014 Angles, scales and parametric renormalization. Zbl 1273.81164Brown, Francis; Kreimer, Dirk 28 2013 Modular forms in quantum field theory. Zbl 1290.81083Brown, Francis; Schnetz, Oliver 19 2013 Iterated integrals in quantum field theory. Zbl 1295.81072Brown, Francis 13 2013 Dedekind zeta motives for totally real number fields. Zbl 1286.14006Brown, Francis C. S. 3 2013 Mixed Tate motives over \(\mathbb{Z}\). Zbl 1278.19008Brown, Francis 137 2012 On the decomposition of motivic multiple zeta values. Zbl 1321.11087Brown, Francis C. S. 65 2012 A \(K3\) in \(\phi^{4}\). Zbl 1253.14024Brown, Francis; Schnetz, Oliver 49 2012 Spanning forest polynomials and the transcendental weight of Feynman graphs. Zbl 1223.05019Brown, Francis; Yeats, Karen 23 2011 Multiple zeta values and periods: from moduli spaces to Feynman integrals. Zbl 1228.81214Brown, Francis 6 2011 The algebra of cell-zeta values. Zbl 1195.14078Brown, Francis; Carr, Sarah; Schneps, Leila 5 2010 Inversion of series and the cohomology of the moduli spaces \({\mathcal M}^\delta_{0,n}\). Zbl 1228.14026Bergström, Jonas; Brown, Francis 4 2010 The massless higher-loop two-point function. Zbl 1196.81130Brown, Francis 56 2009 Multiple zeta values and periods of moduli spaces \(\overline{\mathfrak M}_{0,n}\). Zbl 1216.11079Brown, Francis C. S. 54 2009 On arithmetic and asymptotic properties of up-down numbers. Zbl 1126.05010Brown, Francis C. S.; Fink, Thomas M. A.; Willbrand, Karen 5 2007 Multiple zeta values and periods of moduli spaces \(\bar {\mathfrak M}_{0,n}\). (Périodes des espaces des modules \(\bar {\mathfrak M}_{0,n}\) et valeurs zêtas multiples.) Zbl 1105.11019Brown, Francis C. S. 7 2006 Li’s criterion and zero-free regions of \(L\)-functions. Zbl 1154.11334Brown, Francis C. S. 10 2005 Single-valued multiple polylogarithms in one variable. (Polylogarithmes multiples uniformes en une variable.) Zbl 1048.11053Brown, Francis C. S. 62 2004 all cited Publications top 5 cited Publications all top 5 Cited by 491 Authors 24 Schlotterer, Oliver 19 Duhr, Claude 17 Brown, Francis C. S. 14 McLeod, Andrew J. 13 Panzer, Erik 12 Yeats, Karen A. 11 Dixon, Lance J. 11 Drummond, James M. 10 Brödel, Johannes 10 D’Hoker, Eric 10 von Hippel, Matt 9 Bourjaily, Jacob L. 9 Kleinschmidt, Axel 8 Gardi, Einan 8 Mafra, Carlos R. 8 Matthes, Nils 8 Papathanasiou, Georgios 8 Wilhelm, Matthias 7 Bogner, Christian 7 Dulat, Falko 7 Dupont, Clément 7 Marcolli, Matilde 7 Schnetz, Oliver 7 Tasaka, Koji 7 Vergu, Cristian 7 Weinzierl, Stefan 6 Blümlein, Johannes 6 Caron-Huot, Simon 6 Del Duca, Vittorio 6 Gerken, Jan E. 6 Green, Michael B. 6 He, Song 6 Kreimer, Dirk 6 Stieberger, Stephan 5 Borinsky, Michael 5 Mizera, Sebastian 5 Volk, Matthias 4 Abreu, Samuel 4 Arkani-Hamed, Nima 4 Britto, Ruth 4 Guo, Li 4 Henn, Johannes M. 4 Kaderli, André 4 Kaidi, Justin 4 Li, Jiangtao 4 Marzucca, Robin 4 Omar, Sami 4 Pennington, Jeffrey S. 4 Schabinger, Robert M. 4 Smirnov, Vladimir A. 4 Verbeek, Bram 4 Zhang, Chi 3 Ablinger, Jakob 3 Adams, Luise 3 Bachmann, Henrik 3 Bouillot, Olivier 3 Broadhurst, David John 3 Chang, Chieh-Yu 3 Charlton, Steven 3 Dorigoni, Daniele 3 Eden, Burkhard 3 Hain, Richard M. 3 Herzog, Franz 3 Hessami Pilehrood, Khodabakhsh 3 Hessami Pilehrood, Tatiana 3 Hohenegger, Stefan 3 Klemm, Albrecht 3 Lam, Thomas F. 3 Li, Zhenjie 3 Magnea, Lorenzo 3 Marboe, Christian 3 Mazhouda, Kamel 3 Murty, Maruti Ram 3 Nega, Christoph 3 Ngo Dac, Tuan 3 Pokraka, Andrzej 3 Rasmussen, Christopher 3 Schneider, Carsten 3 Smajlović, Lejla 3 Spradlin, Marcus 3 Sprenger, Martin 3 Straub, Armin 3 Tamagawa, Akio 3 Tancredi, Lorenzo 3 Taylor, Tomasz R. 3 Vanhove, Pierre 3 Volin, Dmytro 3 Von Manteuffel, Andreas 3 Wen, Congkao 3 Willwacher, Thomas Hans 3 Yamamoto, Shuji 3 Yuan, Ellis Ye 2 Alday, Luis Fernando 2 Bargheer, Till 2 Basu, Anirban 2 Bellon, Marc P. 2 Berghoff, Marko 2 Bönisch, Kilian 2 Buring, Ricardo 2 Chen, Huei-Jeng ...and 391 more Authors all top 5 Cited in 98 Serials 141 Journal of High Energy Physics 20 Journal of Number Theory 16 Nuclear Physics. B 13 Letters in Mathematical Physics 10 Communications in Mathematical Physics 10 International Journal of Number Theory 8 Journal of Mathematical Physics 8 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 7 Journal of Algebra 7 Annales de l’Institut Henri Poincaré D. Combinatorics, Physics and their Interactions (AIHPD) 6 Journal of Physics A: Mathematical and Theoretical 6 Research in the Mathematical Sciences 5 Journal of Mathematical Analysis and Applications 5 Mathematische Annalen 5 Transactions of the American Mathematical Society 5 Mathematical Physics, Analysis and Geometry 4 Computer Physics Communications 4 Physics Letters. B 4 Advances in Mathematics 4 Compositio Mathematica 4 Mathematische Zeitschrift 4 Journal de Théorie des Nombres de Bordeaux 4 The Ramanujan Journal 4 Annals of Mathematics. Second Series 3 Discrete Mathematics 3 Physics Reports 3 Inventiones Mathematicae 3 Manuscripta Mathematica 3 Proceedings of the American Mathematical Society 3 Advances in Applied Mathematics 3 Kyushu Journal of Mathematics 3 Selecta Mathematica. New Series 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Algebra & Number Theory 3 Forum of Mathematics, Sigma 3 Research in Number Theory 2 Annales de l’Institut Fourier 2 Journal für die Reine und Angewandte Mathematik 2 Mathematika 2 Nagoya Mathematical Journal 2 Journal of the American Mathematical Society 2 The Electronic Journal of Combinatorics 2 Documenta Mathematica 2 Journal of the European Mathematical Society (JEMS) 2 International Journal of Geometric Methods in Modern Physics 2 Oberwolfach Reports 2 Annales Mathématiques du Québec 1 Modern Physics Letters A 1 International Journal of Modern Physics A 1 American Mathematical Monthly 1 Israel Journal of Mathematics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Physica A 1 Rocky Mountain Journal of Mathematics 1 Journal of Geometry and Physics 1 Fortschritte der Physik 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Canadian Journal of Mathematics 1 Duke Mathematical Journal 1 Functional Analysis and its Applications 1 Geometriae Dedicata 1 The Journal of Symbolic Logic 1 Monatshefte für Mathematik 1 Osaka Journal of Mathematics 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Topology and its Applications 1 European Journal of Combinatorics 1 Constructive Approximation 1 Forum Mathematicum 1 Journal of the Ramanujan Mathematical Society 1 Sugaku Expositions 1 International Journal of Mathematics 1 Annals of Physics 1 Elemente der Mathematik 1 The Australasian Journal of Combinatorics 1 Experimental Mathematics 1 Annales Mathématiques Blaise Pascal 1 Transformation Groups 1 Geometry & Topology 1 Annales Henri Poincaré 1 Journal of Nonlinear Mathematical Physics 1 Algebraic & Geometric Topology 1 Journal of the Australian Mathematical Society 1 Journal of Machine Learning Research (JMLR) 1 JP Journal of Algebra, Number Theory and Applications 1 Journal of the Institute of Mathematics of Jussieu 1 Journal of Noncommutative Geometry 1 Albanian Journal of Mathematics 1 Journal of Singularities 1 Journal of Classical Analysis 1 Journal of Mathematics 1 Mathematics 1 EMS Surveys in Mathematical Sciences 1 Quantum Studies: Mathematics and Foundations 1 European Journal of Mathematics 1 Annals of \(K\)-Theory 1 SIAM Journal on Applied Algebra and Geometry all top 5 Cited in 46 Fields 262 Quantum theory (81-XX) 174 Number theory (11-XX) 79 Algebraic geometry (14-XX) 58 Relativity and gravitational theory (83-XX) 50 Combinatorics (05-XX) 29 Associative rings and algebras (16-XX) 27 Special functions (33-XX) 24 Nonassociative rings and algebras (17-XX) 16 Several complex variables and analytic spaces (32-XX) 16 Mechanics of particles and systems (70-XX) 15 Functions of a complex variable (30-XX) 14 Category theory; homological algebra (18-XX) 10 Differential geometry (53-XX) 9 Commutative algebra (13-XX) 7 Algebraic topology (55-XX) 7 Computer science (68-XX) 6 Manifolds and cell complexes (57-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 \(K\)-theory (19-XX) 5 Partial differential equations (35-XX) 5 Convex and discrete geometry (52-XX) 4 Field theory and polynomials (12-XX) 3 General and overarching topics; collections (00-XX) 3 Group theory and generalizations (20-XX) 3 Ordinary differential equations (34-XX) 3 Difference and functional equations (39-XX) 2 Mathematical logic and foundations (03-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Sequences, series, summability (40-XX) 2 Approximations and expansions (41-XX) 2 Integral transforms, operational calculus (44-XX) 2 Integral equations (45-XX) 2 Geometry (51-XX) 2 Statistics (62-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 History and biography (01-XX) 1 General algebraic systems (08-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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