Ramanujan congruences
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1: 27.14 Unrestricted Partitions
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§27.14(v) Divisibility Properties
… ►Lehmer (1947) conjectures that is never 0 and verifies this for all by studying various congruences satisfied by , for example: …2: Bibliography R
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Congruence properties of partitions.
Math. Z. 9 (1-2), pp. 147–153.
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3: 27.20 Methods of Computation: Other Number-Theoretic Functions
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►A recursion formula obtained by differentiating (27.14.18) can be used to calculate Ramanujan’s function , and the values can be checked by the congruence (27.14.20).
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4: Bibliography K
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Asymptotic expansions of certain -series and a formula of Ramanujan for specific values of the Riemann zeta function.
Acta Arith. 107 (3), pp. 269–298.
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The congruences of Clausen-von Staudt and Kummer for Bernoulli-Hurwitz numbers.
Math. Ann. 216 (1), pp. 1–4.
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The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
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5: Bibliography
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Congruences of -adic integer order Bernoulli numbers.
J. Number Theory 59 (2), pp. 374–388.
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Chapter of Ramanujan’s second notebook: Theta-functions and -series.
Mem. Amer. Math. Soc. 53 (315), pp. v+85.
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Ramanujan Revisited.
Academic Press Inc., Boston, MA.
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Congruences for the -secant numbers.
European J. Combin. 1 (4), pp. 283–287.
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Multiple series Rogers-Ramanujan type identities.
Pacific J. Math. 114 (2), pp. 267–283.
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