First memoir on the asymptotics of certain infinite products
Classical Analysis and ODEs
2024-11-26 v2 Combinatorics
Number Theory
Representation Theory
Abstract
The product sides of the Rogers--Ramanujan identities and alike often appear to be "transparently modular" (functions). The old work by Rogers (1894) and recent work by Rosengren make use (somewhat implicitly) of this fact for proving the identities with the help of underlying modular equationsthe main challenge is verifying the latter for the sum sides. Here we speculate on the potentials of using the asymptotics of such -identities or their finite versions for proving them.
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Cite
@article{arxiv.2411.11100,
title = {First memoir on the asymptotics of certain infinite products},
author = {Wadim Zudilin},
journal= {arXiv preprint arXiv:2411.11100},
year = {2024}
}
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7 pages