Full list of publications: |
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Citations (Crossref Cited-By Service + Math-Net.Ru) |
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1. |
L. D. Faddeev, L. A. Takhtajan, “What is the spin of a spin wave?”, Phys. Lett. A, 85:6-7 (1981), 375–377
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2. |
E. K. Sklyanin, L. A. Takhtadzhyan, L. D. Faddeev, “Quantum inverse problem method. I”, Theoret. and Math. Phys., 40:2 (1979), 688–706 |
3. |
L. A. Takhtadzhyan, L. D. Faddeev, “The quantum method of the inverse problem and the Heisenberg $XYZ$ model”, Russian Math. Surveys, 34:5 (1979), 11–68 |
4. |
V. E. Zakharov, L. A. Takhtadzhyan, “Equivalence of the nonlinear Schrödinger equation and the equation of a Heisenberg ferromagnet”, Theoret. and Math. Phys., 38:1 (1979), 17–23 |
5. |
L. A. Takhtadzhyan, L. D. Faddeev, “Spectrum and scattering of excitations in the one-dimensional isotropic Heisenberg model”, J. Soviet Math., 24:2 (1984), 241–267 |
6. |
L. A. Takhtadzhyan, L. D. Faddeev, “Essentially nonlinear one-dimensional model of classical field theory”, Theoret. and Math. Phys., 21:2 (1974), 1046–1057 |
7. |
V. O. Tarasov, L. A. Takhtadzhyan, L. D. Faddeev, “Local Hamiltonians for integrable quantum models on a lattice”, Theoret. and Math. Phys., 57:2 (1983), 1059–1073 |
8. |
N. Yu. Reshetikhin, L. A. Takhtadzhyan, L. D. Faddeev, “Quantization of Lie groups and Lie algebras”, Leningrad Math. J., 1:1 (1990), 193–225 |
9. |
P. G. Zograf, L. A. Takhtadzhyan, “On uniformization of Riemann surfaces and the Weil-Petersson metric on Teichmüller and Schottky spaces”, Math. USSR-Sb., 60:2 (1988), 297–313 |
10. |
P. G. Zograf, L. A. Takhtadzhyan, “On Liouville's equation, accessory parameters, and the geometry of Teichmüller space for Riemann surfaces of genus 0”, Math. USSR-Sb., 60:1 (1988), 143–161 |
11. |
V. E. Zakharov, L. A. Takhtadzhyan, L. D. Faddeev, “Complete description of solutions of the “sine-Gordon” equation”, Dokl. Akad. Nauk SSSR, 219:6 (1974), 1334–1337 |
12. |
L. A. Takhtadzhyan, “A simple example of modular forms as tau-functions for integrable equations”, Theoret. and Math. Phys., 93:2 (1992), 1308–1317 |
13. |
L. A. Takhtadzhyan, “Quantum inverse scattering method and algebraic matrix Bethe-Ahsatz”, J. Soviet Math., 23:4 (1983), 2470–2486 |
14. |
L. A. Takhtadzhyan, L. D. Faddeev, “The spectral theory of a functional-difference operator in conformal field theory”, Izv. Math., 79:2 (2015), 388–410 |
15. |
P. G. Zograf, L. A. Takhtadzhyan, “A local index theorem for families of $\bar \partial$-operators on Riemann surfaces”, Russian Math. Surveys, 42:6 (1987), 169–190 |
16. |
P. G. Zograf, L. A. Takhtadzhyan, “Action of the Liouville equation is a generating function for the accessory parameters and the potential of the Weil–Petersson metric on the Teichmüller space”, Funct. Anal. Appl., 19:3 (1985), 219–220 |
17. |
A. I. Vinogradov, L. A. Takhtadzhyan, “Theory of Eisenstein series for the group $SL(3,\mathbf R)$ and its application to a binary problem. I. Fourier expansion of the highest Eisenstein series”, J. Soviet Math., 18:3 (1982), 293–324 |
18. |
St. Petersburg Math. J., 6:2 (1994), 429–438 |
19. |
L. A. Takhtadzhyan, “Noncommutative homology of quantum tori”, Funct. Anal. Appl., 23:2 (1989), 147–149 |
20. |
P. G. Zograf, L. A. Takhtadzhyan, “On the geometry of moduli spaces of vector bundles over a Riemann surface”, Math. USSR-Izv., 35:1 (1990), 83–100 |
21. |
L. A. Takhtadzhyan, L. D. Faddeev, “Simple connection between the geometric and the Hamiltonian representations of integrable nonlinear equations”, J. Soviet Math., 28:5 (1985), 800–806 |
22. |
L. A. Takhtajan, A. Yu. Alekseev, I. Ya. Aref'eva, M. A. Semenov-Tian-Shansky, E. K. Sklyanin, F. A. Smirnov, S. L. Shatashvili, “Scientific heritage of L. D. Faddeev. Survey of papers”, Russian Math. Surveys, 72:6 (2017), 977–1081 |
23. |
L. A. Takhtadzhyan, “Real projective connections, V. I. Smirnov's approach, and black-hole-type solutions of the Liouville equation”, Theoret. and Math. Phys., 181:1 (2014), 1307–1316 |
24. |
L. A. Takhtadzhyan, L. D. Faddeev, “Essentially nonlinear one-dimensional model of classical field theory (Addendum)”, Theoret. and Math. Phys., 22:1 (1975), 100 |
25. |
P. G. Zograf, L. A. Takhtadzhyan, “Narasimhan–Seshadri connection and Kähler structure of the space of moduli of holomorphic vector bundles over Riemann surfaces”, Funct. Anal. Appl., 20:3 (1986), 240–241 |
26. |
L. A. Takhtadzhyan, “Solutions of the triangle equations with $\mathbb Z_n\times\mathbb Z_n$-symmetry as the matrix analogues of the Weierstrass zets and sigma functions”, Differential geometry, Lie groups and mechanics. Part VI, Zap. Nauchn. Sem. LOMI, 133, “Nauka”, Leningrad. Otdel., Leningrad, 1984, 258–276 |
27. |
A. I. Vinogradov, L. A. Takhtadzhyan, “On the Linnik–Skubenko asymptotics”, Dokl. Akad. Nauk SSSR, 253:4 (1980), 777–780 |
28. |
L. A. Takhtajan, “Etudes of the resolvent”, Russian Math. Surveys, 75:1 (2020), 147–186 |
29. |
L. A. Takhtajan, “Quantum field theories on algebraic curves. I. Additive bosons”, Izv. Math., 77:2 (2013), 378–406 |
30. |
A. I. Vinogradov, L. A. Takhtadzhyan, “Zeta function of the additive divisor problem and the spectral expansion of the automorphic Laplacian”, Automorphic functions and number theory. Part II, Zap. Nauchn. Sem. LOMI, 134, “Nauka”, Leningrad. Otdel., Leningrad, 1984, 84–116 |
31. |
A. I. Vinogradov, L. A. Takhtadzhyan, “Analogues of the Gauss–Vinogradov formula on the critical line”, J. Soviet Math., 24:2 (1984), 183–208 |
32. |
L. A. Takhtadzhyan, L. D. Faddeev, “The Hamiltonian system connected with the equation $u_{\xi_\eta}+\sin u=0$”, Proc. Steklov Inst. Math., 142 (1979), 277–289 |
33. |
L. A. Takhtadzhyan, “Hamiltonian systems connected with the Dirac equation”, Differential geometry, Lie groups and mechanics, Zap. Nauchn. Sem. LOMI, 37, “Nauka”, Leningrad. Otdel., Leningrad, 1973, 66–76 |
34. |
A. P. Veselov, L. A. Takhtadzhyan, “Integrability of Novikov equations for principal chiral fields with multivalued Lagrangian”, Dokl. Akad. Nauk SSSR, 279:5 (1984), 1097–1100 |
35. |
A. S. Budagov, L. A. Takhtadzhyan, “A nonlinear one-dimensional model of classical field theory with internal degrees of freedom”, Dokl. Akad. Nauk SSSR, 235:4 (1977), 805–808 |
36. |
A. I. Vinogradov, L. A. Takhtadzhyan, “Analogues of the Vinogradov–Gauss formula in the critical strip”, Proc. Steklov Inst. Math., 158 (1983), 47–71 |
37. |
L. A. Takhtadzhyan, “Asymptotic formula for the sum of the lengths of the periods of the quadratic irrationalities of discriminant $D$”, J. Soviet Math., 17:5 (1981), 2173–2181 |
38. |
I. M. Krichever, L. A. Takhtadzhyan, “Algebraic de Rham theorem and Baker–Akhiezer function”, Izv. Math., 88:3 (2024), 506–514 |
39. |
A. Alekseev, S. Shatashvili, L. Takhtajan, “Berezin quantization, conformal welding and the Bott-Virasoro group”, Ann. Henri Poincaré, 25:1 (2024), 35–64 |
40. |
L. A. Takhtajan, “Goldman form, flat connections and stable vector bundles”, Enseign. Math., 68:3-4 (2022), 409–440 |
41. |
L. A. Takhtajan, “Trace formulas for the modified Mathieu equation”, Partial differential equations, spectral theory, and mathematical physics—the Ari Laptev anniversary volume, EMS Ser. Congr. Rep., EMS Press, Berlin, 2021, 427–443 |
42. |
C. Meneses, L. A. Takhtajan, “Logarithmic connections, WZNW action, and moduli of parabolic bundles on the sphere”, Comm. Math. Phys., 387:2 (2021), 649–680 |
43. |
L. A. Takhtajan, “On Kawai theorem for orbifold Riemann surfaces”, Math. Ann., 375:3-4 (2019), 923–947 |
44. |
A. Laptev, L. Schimmer, L. A. Takhtajan, “Weyl asymptotics for perturbed functional difference operators”, J. Math. Phys., 60:10 (2019), 103505 , 10 pp. |
45. |
L. A. Takhtajan, P. Zograf, “Local index theorem for orbifold Riemann surfaces”, Lett. Math. Phys., 109:5 (2019), 1119–1143 |
46. |
J. Park, L. A. Takhtajan, L.-P. Teo, “Potentials and Chern forms for Weil-Petersson and Takhtajan-Zograf metrics on moduli spaces”, Adv. Math., 305 (2017), 856–894 |
47. |
A. Laptev, L. Schimmer, L. A. Takhtajan, “Weyl type asymptotics and bounds for the eigenvalues of functional-difference operators for mirror curves”, Geom. Funct. Anal., 26:1 (2016), 288–305 |
48. |
L. A. Takhtajan, “Explicit computation of the Chern character forms”, Geom. Dedicata, 181 (2016), 223–237 |
49. |
V. P. Pingali, L. A. Takhtajan, “On Bott-Chern forms and their applications”, Math. Ann., 360:1-2 (2014), 519–546 |
50. |
F. Franchini, A. R. Its, V. E. Korepin, L. A. Takhtajan, “Spectrum of the density matrix of a large block of spins of the $XY$ model in one dimension”, Quantum Inf. Process., 10:3 (2011), 325–341 |
51. |
L. A. Takhtajan, Quantum mechanics for mathematicians, Graduate Studies in Mathematics, 95, American Mathematical Society, Providence, RI, 2008 |
52. |
L. A. Takhtajan, P. Zograf, “The first Chern form on moduli of parabolic bundles”, Math. Ann., 341:1 (2008), 113–135 |
53. |
L. D. Faddeev, L. A. Takhtajan, Hamiltonian methods in the theory of solitons, Translated from the 1986 Russian original by Alexey G. Reyman, Classics in Mathematics, English, Springer, Berlin, 2007 |
54. |
A. McIntyre, L. A. Takhtajan, “Holomorphic factorization of determinants of Laplacians on Riemann surfaces and a higher genus generalization of Kronecker's first limit formula”, Geom. Funct. Anal., 16:6 (2006), 1291–1323 |
55. |
L. A. Takhtajan, L.-P. Teo, Weil-Petersson metric on the universal Teichmüller space, Mem. Amer. Math. Soc., 183, no. 861, 2006 , viii+119 pp. |
56. |
L. A. Takhtajan, L.-P. Teo, “Quantum Liouville theory in the background field formalism. I. Compact Riemann surfaces”, Comm. Math. Phys., 268:1 (2006), 135–197 |
57. |
L. A. Takhtajan, “Free bosons and dispersionless limit of Hirota tau-function”, Bilinear integrable systems: from classical to quantum, continuous to discrete, NATO Sci. Ser. II Math. Phys. Chem., 201, Springer, Dordrecht, 2006, 301–311 |
58. |
L. A. Takhtajan, L.-P. Teo, “Weil-Petersson geometry of the universal Teichmüller space”, Infinite dimensional algebras and quantum integrable systems, Progr. Math., 237, Birkhäuser, Basel, 2005, 225–233 |
59. |
L. A. Takhtajan, L.-P. Teo, “Liouville action and Weil-Petersson metric on deformation spaces, global Kleinian reciprocity and holography”, Comm. Math. Phys., 239:1-2 (2003), 183–240 |
60. |
L. Takhtajan, P. Zograf, “Hyperbolic 2-spheres with conical singularities, accessory parameters and Kähler metrics on $\mathcal{M}_{0,n}$”, Trans. Amer. Math. Soc., 355:5 (2003), 1857–1867 |
61. |
E. Aldrovandi, L. A. Takhtajan, “Generating functional in CFT on Riemann surfaces. II. Homological aspects”, Comm. Math. Phys., 227:2 (2002), 303–348 |
62. |
L. A. Takhtajan, “Free bosons and tau-functions for compact Riemann surfaces and closed smooth Jordan curves. Current correlation functions”, EuroConférence Moshé Flato 2000, Part III (Dijon), Letters in Mathematical Physics, 56, 2001, 181–228 |
63. |
L. A. Takhtajan, “Quantum field theories on an algebraic curve [MR1800492 (2001m:81267)]”, Conférence Moshé Flato 1999 (Dijon), v. I, Math. Phys. Stud., 21, Kluwer Acad. Publ., Dordrecht, 2000, 403–416 |
64. |
L. A. Takhtajan, “Quantum field theories on an algebraic curve”, Conference Moshé Flato 1999 (Dijon), Letters in Mathematical Physics, 52, 2000, 79–91 |
65. |
N. Reshetikhin, L. A. Takhtajan, “Deformation quantization of Kähler manifolds”, L. D. Faddeev's Seminar on Mathematical Physics, Amer. Math. Soc. Transl. Ser. 2, 201, Amer. Math. Soc., Providence, RI, 2000, 257–276 |
66. |
E. Aldrovandi, L. A. Takhtajan, “Generating functional in CFT and effective action for two-dimensional quantum gravity on higher genus Riemann surfaces”, Comm. Math. Phys., 188:1 (1997), 29–67 |
67. |
G. Dito, M. Flato, D. Sternheimer, L. Takhtajan, “Deformation quantization and Nambu mechanics”, Comm. Math. Phys., 183:1 (1997), 1–22 |
68. |
Y. L. Daletskii, L. A. Takhtajan, “Leibniz and Lie algebra structures for Nambu algebra”, Lett. Math. Phys., 39:2 (1997), 127–141 |
69. |
L. A. Takhtajan, “Integrable cellular automata and AKNS hierarchy”, Symmetries and integrability of difference equations (Estérel, PQ, 1994), CRM Proc. Lecture Notes, 9, Amer. Math. Soc., Providence, RI, 1996, 371–375 |
70. |
L. A. Takhtajan, “Topics in the quantum geometry of Riemann surfaces: two-dimensional quantum gravity”, Quantum groups and their applications in physics (Varenna, 1994), Proc. Internat. School Phys. Enrico Fermi, 127, IOS, Amsterdam, 1996, 541–579 |
71. |
R. Chatterjee, L. Takhtajan, “Aspects of classical and quantum Nambu mechanics”, Lett. Math. Phys., 37:4 (1996), 475–482 |
72. |
L. A. Takhtajan, “Equivalence of geometric $h<1/2$ and standard $c>25$ approaches to two-dimensional quantum gravity”, Modern Phys. Lett. A, 11:2 (1996), 93–101 |
73. |
L. A. Takhtajan, “Elementary course on quantum groups”, Lectures on integrable systems (Sophia-Antipolis, 1991), World Sci. Publ., River Edge, NJ, 1994, 319–347 |
74. |
L. A. Takhtajan, “Liouville theory: Ward identities for generating functional and modular geometry”, Modern Phys. Lett. A, 9:25 (1994), 2293–2299 |
75. |
L. Takhtajan, “On foundation of the generalized Nambu mechanics”, Comm. Math. Phys., 160:2 (1994), 295–315 |
76. |
L. A. Takhtajan, “Elementary introduction to quantum groups”, Important developments in soliton theory, Springer Ser. Nonlinear Dynam., Springer, Berlin, 1993, 441–467 |
77. |
L. A. Takhtajan, “Modular forms as $\tau$-functions for certain integrable reductions of the Yang-Mills equations”, Integrable systems (Luminy, 1991), Progr. Math., 115, Birkhäuser Boston, Boston, MA, 1993, 115–129 |
78. |
M. J. Ablowitz, S. Chakravarty, L. A. Takhtajan, “A self-dual Yang-Mills hierarchy and its reductions to integrable systems in $1+1$ and $2+1$ dimensions”, Comm. Math. Phys., 158:2 (1993), 289–314 |
79. |
M. J. Ablowitz, S. Chakravarty, L. Takhtajan, “Integrable systems, self-dual Yang-Mills equations and connections with modular forms”, Nonlinear problems in engineering and science—numerical and analytical approach (Beijing, 1991), Sci. Press Beijing, Beijing, 1992, 1–15 |
80. |
L. Takhtajan, “Semi-classical Liouville theory, complex geometry of moduli spaces, and uniformization of Riemann surfaces”, New symmetry principles in quantum field theory (Cargèse, 1991), NATO Adv. Sci. Inst. Ser. B: Phys., 295, Plenum, New York, 1992, 383–406 |
81. |
S. Chakravarty, M. J. Ablowitz, L. A. Takhtajan, “Self-dual Yang-Mills equation and new special functions in integrable systems”, Nonlinear evolution equations and dynamical systems (Baia Verde, 1991), World Sci. Publ., River Edge, NJ, 1992, 3–11 |
82. |
L. A. Takhtajan, P. G. Zograf, “A local index theorem for families of $\overline\partial$-operators on punctured Riemann surfaces and a new Kähler metric on their moduli spaces”, Comm. Math. Phys., 137:2 (1991), 399–426 |
83. |
L. A. Takhtajan, “Introduction to quantum groups”, Quantum groups (Clausthal, 1989), v. 370, Lecture Notes in Phys., Springer, Berlin, 1990, 3–28 |
84. |
L. A. Takhtajan, “Lectures on quantum groups”, Introduction to quantum group and integrable massive models of quantum field theory (Nankai, 1989), Nankai Lectures Math. Phys., World Sci. Publ., River Edge, NJ, 1990, 69–197 |
85. |
L. Faddeev, N. Reshetikhin, L. Takhtajan, “Quantum groups”, Braid group, knot theory and statistical mechanics, v. 9, Adv. Ser. Math. Phys., World Sci. Publ., Teaneck, NJ, 1989, 97–110 |
86. |
L. A. Takhtajan, “Quantum groups and integrable models”, Integrable systems in quantum field theory and statistical mechanics, Adv. Stud. Pure Math., 19, Academic Press, Boston, MA, 1989, 435–457 |
87. |
L. A. Takhtajan, “Uniformization, local index theorem, and geometry of the moduli spaces of Riemann surfaces and vector bundles”, Theta functions—Bowdoin 1987 (Brunswick, ME, 1987), v. 1, Proc. Sympos. Pure Math., 49, no. 1, Amer. Math. Soc., Providence, RI, 1989, 581–596 |
88. |
L. A. Takhtajan, P. G. Zograf, “The Selberg zeta function and a new Kähler metric on the moduli space of punctured Riemann surfaces”, J. Geom. Phys., 5:4 (1988), 551–570 |
89. |
L. D. Faddeev, N. Y. Reshetikhin, L. A. Takhtajan, “Quantization of Lie groups and Lie algebras”, Algebraic analysis, v. I, Academic Press, Boston, MA, 1988, 129–139 |
90. |
P. G. Zograf, L. A. Takhtadzhyan, “The potential of the Weil-Petersson metric on Torelli space”, Analytical theory of numbers and theory of functions. Part 8, Zap. Nauchn. Sem. LOMI, 160, “Nauka”, Leningrad. Otdel., Leningrad, 1987, 110–120 |
91. |
L. D. Faddeev, L. A. Takhtajan, Hamiltonian methods in the theory of solitons, Translated from the Russian by A. G. Reyman [A. G. Reĭman], Springer Series in Soviet Mathematics, Springer-Verlag, Berlin, 1987 |
92. |
L. A. Takhtadzhyan, L. D. Faddeev, Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 , 527 pp. |
93. |
L. D. Faddeev, L. A. Takhtajan, “Liouville model on the lattice”, Field theory, quantum gravity and strings (Meudon/Paris, 1984/1985), Lecture Notes in Phys., 246, Springer, Berlin, 1986, 166–179 |
94. |
L. A. Takhtajan, “Introduction to algebraic Bethe ansatz”, Exactly solvable problems in condensed matter and relativistic field theory (Panchgani, 1985), Lecture Notes in Phys., 242, Springer, Berlin, 1985, 175–219 |
95. |
L. A. Takhtadzhyan, “Application of spectral methods to the arithmetic of real quadratic fields”, Proc. Steklov Inst. Math., 163 (1985), 265–267 |
96. |
L. A. Takhtajan, “Integrable models in classical and quantum field theory”, Proceedings of the International Congress of Mathematicians (Warsaw, 1983), v. 1, 2, PWN, Warsaw, 1984, 1331–1346 |
97. |
A. I. Vinogradov, L. A. Takhtadzhyan, “An estimate of the residue of Rankin $L$-series”, Dokl. Akad. Nauk SSSR, 267:1 (1982), 30–34 |
98. |
A. I. Vinogradov, L. A. Takhtadzhyan, “On the Gauss–Hasse conjecture for real quadratic fields”, Dokl. Akad. Nauk SSSR, 255:6 (1980), 1306–1309 |
99. |
L. A. Takhtadzhyan, A. I. Vinogradov, “On analogues of the Vinogradov-Gauss formula”, Dokl. Akad. Nauk SSSR, 254:6 (1980), 1298–1301 |
100. |
I. Ya. Aref'eva, V. M. Buchstaber, E. P. Velikhov, A. B. Zhizhchenko, V. E. Zakharov, I. A. Ibragimov, S. V. Kislyakov, V. V. Kozlov, P. P. Kulish, L. N. Lipatov, V. P. Maslov, V. A. Matveev, S. P. Novikov, Yu. S. Osipov, A. M. Polyakov, V. A. Rubakov, M. A. Semenov-Tian-Shansky, Yu. A. Simonov, Ya. G. Sinai, A. A. Slavnov, I. A. Sokolov, L. A. Takhtadzhyan, V. E. Fortov, S. L. Shatashvili, “Ludvig Dmitrievich Faddeev (on his 80th birthday)”, Russian Math. Surveys, 69:6 (2014), 1133–1142 |
101. |
I. Ya. Aref'eva, V. E. Zakharov, V. V. Kozlov, I. M. Krichever, V. P. Maslov, S. P. Novikov, A. M. Polyakov, N. Yu. Reshetikhin, M. A. Semenov-Tian-Shansky, E. K. Sklyanin, F. A. Smirnov, L. A. Takhtajan, S. L. Shatashvili, “Ludwig Dmitrievich Faddeev (obituary)”, Russian Math. Surveys, 72:6 (2017), 1157–1163 |
102. |
Differentsialnaya geometriya, gruppy Li i mekhanika. VI, Zap. nauchn. sem. LOMI, 133, ed. A. B. Venkov, L. A. Takhtadzhyan, Izd-vo «Nauka», Leningrad. otd., L., 1984 , 312 pp. |
103. |
Avtomorfnye funktsii i teoriya chisel. II, Zap. nauchn. sem. LOMI, 134, ed. A. B. Venkov, A. I. Vinogradov, L. A. Takhtadzhyan, Izd-vo «Nauka», Leningrad. otd., L., 1984 , 260 pp. |
104. |
Analiticheskaya teoriya chisel i teoriya funktsii. 2, Zap. nauchn. sem. LOMI, 91, ed. A. B. Venkov, L. A. Takhtadzhyan, Izd-vo «Nauka», Leningrad. otd., L., 1979 , 184 pp. |
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