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CONGRUENCES MODULO 4 FOR WEIGHT $\textbf{3/2}$ ETA-PRODUCTS

Part of: Discontinuous groups and automorphic forms Forms and linear algebraic groups

Published online by Cambridge University Press:  05 October 2020

RONG CHEN Open the ORCID record for RONG CHEN [Opens in a new window]  and
F. G. GARVAN Open the ORCID record for F. G. GARVAN [Opens in a new window]
RONG CHEN*
Affiliation:
School of Mathematical Sciences, East China Normal University, Shanghai, People’s Republic of China
F. G. GARVAN
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL32611-8105, USA e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

We find and prove a class of congruences modulo 4 for eta-products associated with certain ternary quadratic forms. This study was inspired by similar conjectured congruences modulo 4 for certain mock theta functions.

Keywords

ternary quadratic formsRamanujan-type congruences

MSC classification

Primary: 11E20: General ternary and quaternary quadratic forms; forms of more than two variables
Secondary: 11F33: Congruences for modular and $p$-adic modular forms
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 3 , June 2021 , pp. 405 - 417
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

The second author was supported in part by a grant from the Simons Foundation (#318714).

References

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