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Sieves for theorems of Euler, Rogers, and Ramanujan

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The Theory of Arithmetic Functions

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 251))

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References

  1. G. E. Andrews, An analytic proof of the Rogers-Ramanujan-Gordon identities, Amer. J. Math. 88 (1966), 844–846.

    Article  MathSciNet  MATH  Google Scholar 

  2. G. E. Andrews, A polynomial identity which implies the Rogers-Ramanujan identities, Scripta Math. 23 (1970), 297–305.

    MATH  Google Scholar 

  3. A. O. L. Atkin and H. P. F. Swinnerton-Dyer, Some properties of partitions, Proc. London Math. Soc. (3) 4 (1954), 84–106.

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  4. A. O. L. Atkin, A note on ranks and conjugacy of partitions, Quart. J. Math. Oxford Ser. (2) 17 (1966), 335–338.

    Article  MathSciNet  MATH  Google Scholar 

  5. F. J. Dyson, Some guesses in the theory of partitions, Eureka 8 (1944), 10–15.

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  6. B. Gordon, A combinatorial generalization of the Rogers-Ramanujan identities, Amer. J. Math. 83 (1961), 393–399.

    Article  MathSciNet  MATH  Google Scholar 

  7. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Fourth Edition, Oxford University Press, Oxford, 1960.

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  8. W. J. LeVeque, Topics in Number Theory, Vol. 1, Addison-Wesley, Reading, 1956.

    MATH  Google Scholar 

  9. I. J. Schur, Ein Beitag zur additiven Zahlentheorie, Sitzungsber. Akad. Wissensch., Berlin, Phys.-Math. Kl., 1917, 302–321.

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  10. J. J. Sylvester, A constructive theory of partitions, arranged in three acts, an interact, and an exodion, Amer. J. Math. 5 (1882), 251–330.

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Anthony A. Gioia Donald L. Goldsmith

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© 1972 Springer-Verlag

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Andrews, G.E. (1972). Sieves for theorems of Euler, Rogers, and Ramanujan. In: Gioia, A.A., Goldsmith, D.L. (eds) The Theory of Arithmetic Functions. Lecture Notes in Mathematics, vol 251. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058782

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  • DOI: https://doi.org/10.1007/BFb0058782

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  • Print ISBN: 978-3-540-05723-9

  • Online ISBN: 978-3-540-37098-7

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