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ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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A matrix free treatment of the problem of Riemann matrices
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by L. Auslander and R. Tolimieri PDF
Bull. Amer. Math. Soc. 5 (1981), 263-312
References
    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. Adrian Albert, Algebras of degree $2^e$ and pure Riemann matrices, Ann. of Math. (2) 33 (1932), no. 2, 311–318. MR 1503054, DOI 10.2307/1968332
  • A. Adrian Albert, On the construction of Riemann matrices. I, Ann. of Math. (2) 35 (1934), no. 1, 1–28. MR 1503140, DOI 10.2307/1968116
  • A. Adrian Albert, On the construction of Riemann matrices. II, Ann. of Math. (2) 36 (1935), no. 2, 376–394. MR 1503230, DOI 10.2307/1968578
  • A. Adrian Albert, A solution of the principal problem in the theory of Riemann matrices, Ann. of Math. (2) 35 (1934), no. 3, 500–515. MR 1503176, DOI 10.2307/1968747
  • A. Adrian Albert, Involutorial simple algebras and real Riemann matrices, Ann. of Math. (2) 36 (1935), no. 4, 886–964. MR 1503260, DOI 10.2307/1968595
    • 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.
  • Pierre Cartier, Quantum mechanical commutation relations and theta functions, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 361–383. MR 0216825
  • Helmut Hasse, Theory of cyclic algebras over an algebraic number field, Trans. Amer. Math. Soc. 34 (1932), no. 1, 171–214. MR 1501634, DOI 10.1090/S0002-9947-1932-1501634-5
    • 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, Ueber algebraische Correspondenzen und das verallgemeinerte Correspondenzprincip, Math. Ann. 28 (1887), no. 4, 561–585 (German). MR 1510394, DOI 10.1007/BF01447915
    • S. Lefschetz, 18. Selected topics in algebraic geometry, Bull. of N.B.C., No. 63, Washington, 1928 (reprinted, Chelsea, 1970).
  • Solomon Lefschetz, On certain numerical invariants of algebraic varieties with application to abelian varieties, Trans. Amer. Math. Soc. 22 (1921), no. 3, 327–406. MR 1501178, DOI 10.1090/S0002-9947-1921-1501178-3
    • H. Poincaré, 20. Sur la réduction des intégrales Abéliennes, Oeuvres t. III (1934), 333-351.
  • Harry E. Rauch and Aaron Lebowitz, Elliptic functions, theta functions, and Riemann surfaces, Williams & Wilkins Co., Baltimore, Md., 1973. MR 0349993
  • Harry E. Rauch and Hershel M. Farkas, Theta functions with applications to Riemann surfaces, Williams & Wilkins Co., Baltimore, Md., 1974. MR 0352108
    • 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, Lectures on Riemann matrices, Tata Institute of Fundamental Research Lectures on Mathematics, No. 28, Tata Institute of Fundamental Research, Bombay, 1963. Notes by S. Raghavan and S. S. Rangachari. MR 0266959
  • J. H. M. Wedderburn, On division algebras, Trans. Amer. Math. Soc. 22 (1921), no. 2, 129–135. MR 1501164, DOI 10.1090/S0002-9947-1921-1501164-3
  • AndrĂ© Weil, Sur certains groupes d’opĂ©rateurs unitaires, Acta Math. 111 (1964), 143–211 (French). MR 165033, DOI 10.1007/BF02391012
  • Hermann Weyl, On generalized Riemann matrices, Ann. of Math. (2) 35 (1934), no. 4, 714–729. MR 1503189, DOI 10.2307/1968487
  • Hermann Weyl, Generalized Riemann matrices and factor sets, Ann. of Math. (2) 37 (1936), no. 3, 709–745. MR 1503306, DOI 10.2307/1968485
    • 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.
  • Carl Ludwig Siegel, Die Modulgruppe in einer einfachen involutorischen Algebra, Festschrift zur Feier des zweihundertjährigen Bestehens der Akademie der Wissenschaften in Göttingen. I. Math.-Phys. Kl., Springer-Verlag, Berlin-Göttingen-Heidelberg, 1951, pp. 157–167 (German). MR 0052460
  • AndrĂ© Weil, Algebras with involutions and the classical groups, J. Indian Math. Soc. (N.S.) 24 (1960), 589–623 (1961). MR 136682
  • Goro Shimura, Introduction to the arithmetic theory of automorphic functions, KanĂ´ Memorial Lectures, No. 1, Iwanami Shoten Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971. Publications of the Mathematical Society of Japan, No. 11. MR 0314766
  • Goro Shimura and Yutaka Taniyama, Complex multiplication of abelian varieties and its applications to number theory, Publications of the Mathematical Society of Japan, vol. 6, Mathematical Society of Japan, Tokyo, 1961. MR 0125113
  • David Mumford, Curves and their Jacobians, University of Michigan Press, Ann Arbor, Mich., 1975. MR 0419430
  • Nathan Jacobson, Abraham Adrian Albert (1905–1972), Bull. Amer. Math. Soc. 80 (1974), 1075–1100. MR 342341, DOI 10.1090/S0002-9904-1974-13622-0
    • 1. A. A. Albert, Structures of algebras, Amer. Math. Soc. Colloq. Publ., no. 24, Amer. Math. Soc. Providence, R. I., 1939.
  • Louis Auslander, Lecture notes on nil-theta functions, Regional Conference Series in Mathematics, No. 34, American Mathematical Society, Providence, R.I., 1977. MR 0466409, DOI 10.1090/cbms/034
  • Nathan Jacobson, Abraham Adrian Albert (1905–1972), Bull. Amer. Math. Soc. 80 (1974), 1075–1100. MR 342341, DOI 10.1090/S0002-9904-1974-13622-0
  • C. L. Siegel, Lectures on Riemann matrices, Tata Institute of Fundamental Research Lectures on Mathematics, No. 28, Tata Institute of Fundamental Research, Bombay, 1963. Notes by S. Raghavan and S. S. Rangachari. MR 0266959
  • R. Tolimieri, Heisenberg manifolds and theta functions, Trans. Amer. Math. Soc. 239 (1978), 293–319. MR 487050, DOI 10.1090/S0002-9947-1978-0487050-7
  • AndrĂ© Weil, Sur certains groupes d’opĂ©rateurs unitaires, Acta Math. 111 (1964), 143–211 (French). MR 165033, DOI 10.1007/BF02391012
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Additional Information
  • Journal: Bull. Amer. Math. Soc. 5 (1981), 263-312
  • MSC (1980): Primary 01A55, 01A60, 16A46, 22E25
  • DOI: https://doi.org/10.1090/S0273-0979-1981-14935-1
  • MathSciNet review: 628660