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Ramanujan–Weber Class Invariant G n And Watson's Empirical Process
Author(s) -
Chan Heng Huat
Publication year - 1998
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610798006127
Subject(s) - watson , ramanujan's sum , mathematics , kronecker delta , class (philosophy) , combinatorics , invariant (physics) , pure mathematics , mathematical physics , philosophy , epistemology , physics , computer science , quantum mechanics , natural language processing
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 G 1353 . 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 G n .