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RAMANUJAN–WEBER CLASS INVARIANT Gn AND WATSON'S EMPIRICAL PROCESS

Published online by Cambridge University Press:  01 June 1998

HENG HUAT CHAN
HENG HUAT CHAN
Affiliation:
Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 119260
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Abstract

In an attempt to prove all the identities given in Ramanujan's first two letters to G. H. Hardy, G. N. Watson devoted a paper to the evaluation of G1353. At the end of his paper, Watson remarked that his proof was not rigorous as he had assumed certain identities (see (1.1) and (1.2)) which he found empirically. In this paper, we use class field theory, Galois theory and Kronecker's limit formula to justify Watson's assumptions. We shall then use our results to compute some new values of Gn.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 57 , Issue 3 , June 1998 , pp. 545 - 561
Copyright
The London Mathematical Society 1998

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