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A PROOF OF HIRSCHHORN’S CONJECTURE ON $2^n$-DISSECTION OF EULER’S PRODUCT

Published online by Cambridge University Press:  08 October 2024

BIPUL KUMAR SARMAH*
Affiliation:
Department of Mathematical Sciences, Tezpur University, Napaam 784028, Sonitpur, Assam, India
SATYAJIT GAYAN
Affiliation:
Department of Mathematical Sciences, Tezpur University, Napaam 784028, Sonitpur, Assam, India e-mail: [email protected]

Abstract

Using properties of Ramanujan’s theta functions, we give an elementary proof of Hirschhorn’s conjecture on $2^n$-dissection of Euler’s product $E(q):=(q;q)_\infty $.

Type
Research Article
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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