Proofs of some conjectures of Sun on the relations between \(T(a, b, c, d; n)\) and \(N(a, b, c, d; n)\)

DOI10.1216/RMJ.2022.52.829zbMath1497.11091OpenAlexW4283078779WikidataQ113751465 ScholiaQ113751465MaRDI QIDQ2153772

Bernard L. S. Lin, Liping Cao

Publication date: 13 July 2022

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-52/issue-3/Proofs-of-some-conjectures-of-Sun-on-the-relations-between/10.1216/rmj.2022.52.829.full

zbMATH Keywords

theta function identitiessum of squaressum of triangular numbers

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Representation problems (11D85)

Related Items (2)

Proofs of some conjectures of Sun on the relations between \(t(a, b, c; n)\) and \(N(a, b, c; n)\) ⋮ Proofs of some conjectures of Sun on representations by linear combinations of triangular numbers

Cites Work

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• Some new old-fashioned modular identities
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• Proofs of some conjectures of Z.-H. Sun on relations between sums of squares and sums of triangular numbers
• The relations between \(N(a,b,c,d;n)\) and \(t(a,b,c,d;n)\) and (\(p,k\))-parametrization of theta functions
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• Some relations between $t(a,b,c,d;n)$ and $N(a,b,c,d;n)$
• SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS INDUCED BY PARTITIONS OF 8
• Proofs of some conjectures of Sun on the relations between sums of squares and sums of triangular numbers
• The number of representations of n as a linear combination of triangular numbers
• Ramanujan’s theta functions and sums of triangular numbers
• A GENERAL RELATION BETWEEN SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS

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