Bulletin of the American Mathematical Society

Author(s): L. Auslander; R. Tolimieri
Journal: Bull. Amer. Math. Soc. 5 (1981), 263-312.
MSC (1980): Primary 01A55, 01A60, 16A46, 22E25
MathSciNet review: 628660
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A. A. Albert, 1. Structures of algebras, Amer. Math. Soc. Colloq. Publ., vol. 24, Amer. Math. Soc., Providence, R. I., 1939.; A. A. Albert, 2. On the structure of pure Riemann matrices with non-commutative multiplication algebras, Palermo Rendiconti 55 (1931), 57-115.; A. A. Albert, 3. Algebras of degree 2, Ann. of Math. (2) 33 (1932), 311-318. MR 1503054; A. A. Albert, 4. On the construction of Riemann matrices. I, Ann. of Math. (2) 35 (1934), 1-18. MR 1503140; A. A. Albert, 5. On the construction of Riemann matrices. II, Ann. of Math. (2) 36 (1935), 376-394. MR 1503230; A. A. Albert, 6. A solution of the principal problem in the theory of Riemann matrices, Ann. of Math. (2) 35 (1934) 500-515. MR 1503176; A. A. Albert, 7. Involutorial simple algebras and real Riemann matrices, Ann. of Math. (2) 36 (1935), 886-964. MR 1503260; H. F. Baker, 8. An introduction to the theory of multiply periodic functions, Cambridge, 1 (1907).; R. Brauer, H. Hasse, E. Noether, 9. Beweis eines Heuptsatzes in der Theorie der Algebren, Crellés J. 167 (1931), 399-404.; P. Cartier, 10. Quantum mechanical commutative relations and theta functions, Proc. Sympos. Pure Math., vol. 9, Amer. Math. Soc., Providence, R. I., 1965, pp. 361-387. MR 216825; H. Hasse, 11. Theory of cyclic algebra over an algebraic number field, Trans. Amer. Math. Soc. 34 (1932), 170-214. MR 1501634; G. Humbert, 12. Sur les fonction abéliennes singulières, J. de Math. (5) 5 (1899), 233-350.; G. Humbert, 13. Sur les fonction abéliennes singulières, J. de Math. (5) 6 (1900), 279-386.; G. Humbert, 14. Sur les fonction abéliennes singulières, J. de Math. 7 (1901), 97-123.; A. Hurwitz, 15. Zur Theorie der Modulargleichungen, Gott. Nach. (1883), 350-363.; A. Hurwitz, 16. Über Algebraische Korrespondensen und dos Verallegemeinerte Korrespondenzprinzip, Leipz. Ab. (1886), 10-38.; A. Hurwitz, 17. Über Algebraische Korresponenzen und dos Verallgemeinerte Korrespondenzprinzip, Math. Ann 28 (1887), 561-585. MR 1510394; S. Lefschetz, 18. Selected topics in algebraic geometry, Bull. of N.B.C., No. 63, Washington, 1928 (reprinted, Chelsea, 1970).; S. Lefschetz, 19. On certain numerical invariants of algebraic varieties with applications to abelian varieties, Trans. Amer. Math. Soc. 22 (1921) 327-482; translation of the memoir awarded the Bordin Prize by the Paris Academy of Sciences for the year 1919. MR 1501178; H. Poincaré, 20. Sur la réduction des intégrales Abéliennes, Oeuvres t. III (1934), 333-351.; H. Rauch and A. Leibowitz, 21. Elliptic functions, theta functions and Riemann surfaces, Williams & Wilkins Co., Baltimore, Maryland, 1973. MR 349993; H. Rauch and H. Farkas, 22. Theta functions with applications to Riemann surfaces, Williams & Wilkins Co., Baltimore, Maryland, 1974. MR 352108; B. Riemann, 23. Theorie der abelschen Funktionen, Gesamm. Math. Werke, Dover, New York, 1953, pp. 84-142.; C. Rosati, 24. Sulle corrispondenze plurivalenti fra i punti di una curva algebrica, Atti Accad. Sci. Torino 51 (1915-16), 991-1014.; C. Rosati, 25. Sulle valenze delle corrispondenze algebriche fra i punti di una curva algebrica, ibid. 53 (1917-18), 5-22.; C. Rosati, 26. Intorno alle corrispondenze simmetriche singolari sopra una curva di genere 2, Rend. Circ. Mat. Palermo 44 (1920), 307-335.; C. Rosati, 27. Sulle corrispondenze fra i punti di una curva algebrica e, in particolare, fra i punti di una curva di genere due, Ann. Mat. Pura Appl. (3) 25 (1916), 1-32.; C. Rosati, 28. Sulle corrispondenze algebriche fra i punti di due curve algebriche, ibid. (3) 28 (1918), 35-60.; C. Rosati, 29. Sulle corrispondenze algebriche fra i punti di una curva algebrica, Atti Accad. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (5) 22 (1913), 2° Semestre, 385-390, 431-436.; C. Rosati, 30. Sulle corrispondenze fra i punti di una curva algebrica e, in particolare, fra i punti di una curva di genere due, ibid. (5) 24 (1915), 2° Semestre, 182-184.; C. Rosati, 31. Sulle matrici di Riemann, Rend Circ. Mat. Palermo 53 (1929), 79-134.; G. Scorza, 32. Sopra alcune notevoli madrici riemanniane, Torino Atti. 53 (1917), 1008-1017.; G. Scorza, 33. Intorno alla teoria generale della matrici di Riemann, Rend. Circ. Mat. Palermo 41 (1916), 263-379.; G. Scorza, 34. Le algebre di ordine qualunque e le matrici di Riemann, Rend. Circ. Mat. Palermo, 45 (1921), 1-204.; G. Scorza, 35. Papers from 1914-1916, Rom. Acc. L. Rend.; C. L. Siegel, 36. Lectures on Riemann matrices, Tata Institute of Fundamental Research, Bombay, 1963. MR 266959; J. H. M. Wedderburn, 37. On division algebras, Trans. Amer. Math. Soc. 22 (1921), 129-135. MR 1501164; A. Weil, 38. Sur certaine groupes d'operateurs unitaires, Acta. Math. 111 (1964), 143-211. MR 165033; H. Weyl, 39. On generalized Riemann matrices, Ann. of Math. (2) 35 (1934), 714-729. MR 1503189; H. Weyl, 40. Generalized Riemann matrices and factor sets, Ann. of Math. (2) 37 (1936), 704-745. MR 1503306; E. T. Whittaker and G. N. Watson, 41. A course of modern analysis, Cambridge, 1902.; I. C. L. Siegel, Advanced topics in analytic number theory, Tata Institute of Fundamental Research, Bombay, India, 1961.; I. C. L. Siegel, Die Modulgruppe in einer einfachen involutorischen algebra, Festschrift Akad. Miss. Gottingen, 1951. MR 52460; II. A. Weil, Algebras with involutions and the classical groups, J. Indian. Math. Soc. 24 (1960), 589-623. MR 136682; III. G. Shimura, Introduction to the arithmetic theory of automorphic functions, Kanô Memorial Lectures No. 1 Iwanami Shoten, Publishers and Princeton University Press, 1971. MR 314766; III. G. Shimura and Y. Taniyama, Complex multiplications of Abelian varieties and its applications to number theory, Publ. Math. Soc. Japan no. 6, 1961. MR 125113; IV. D. Mumford, Curves and their Jacobians, University of Michigan Press, Ann Arbor, 1976. MR 419430; V. N. Jacobson, Abraham Adrian Albert 1905-1972, Bull. Amer. Math. Soc. 80 (1974), 1075-1100. MR 342341
1.: A. A. Albert, Structures of algebras, Amer. Math. Soc. Colloq. Publ., no. 24, Amer. Math. Soc. Providence, R. I., 1939.
2.: L. Auslander, Lecture notes on nil-theta functions, CBMS Regional Conf. Ser. in Math., no. 34, Amer. Math. Soc., Providence, R. I., 1977. MR 466409
3.: N. Jacobson, Abraham Adrian Albert 1905-1972, Bull. Amer. Math. Soc. 80 (1974), 1075-1100. MR 342341
4.: C. L. Siegel, Lectures on Riemann matrices, Tata Institute of Fundamental Research, Bombay, 1963. MR 266959
5.: R. Tolimieri, Heisenberg manifolds and theta functions, Trans. Amer. Math. Soc. 239 (1978), 293-319. MR 487050
6.: A. Weil. Sur certaines groupes d'operateurs unitaires, Acta Math. 111 (1964), 143-211. MR 165033

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