Proofs of some conjectures of Sun on the relations between sums of squares and sums of triangular numbers

DOI10.1142/S1793042119500088zbMath1459.11099OpenAlexW2888314411WikidataQ113776675 ScholiaQ113776675MaRDI QIDQ4623475

Ernest X. W. Xia, Zhang Yan

Publication date: 15 February 2019

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042119500088

zbMATH Keywords

sum of squaresRamanujan's theta function identitiessum of triangular numbers

Mathematics Subject Classification ID

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

Related Items (10)

On conjectures of Z.-H. Sun ⋮ Explicit congruences modulo 2048 for overpartitions ⋮ Proofs of some conjectures of Sun on the relations between \(T(a, b, c, d; n)\) and \(N(a, b, c, d; n)\) ⋮ Automatic proofs of some conjectures of Sun on the relations between sums of squares and sums of triangular numbers ⋮ Proofs of some conjectures of Sun on the relations between \(t(a, b, c; n)\) and \(N(a, b, c; n)\) ⋮ Unnamed Item ⋮ Ramanujan’s theta function identities and the relations between sums of squares and sums of triangular numbers ⋮ New congruences modulo 5 and 9 for partitions with odd parts distinct ⋮ Parity results for broken 11-diamond partitions ⋮ Proofs of some conjectures on the reciprocals of the Ramanujan-Gordon identities

Cites Work

• Unnamed Item
• Some modular relations for the Göllnitz-Gordon functions by an even-odd method
• Arithmetic properties of partitions with odd parts distinct
• The number of representations of a positive integer by certain octonary quadratic forms
• The relations between \(N(a,b,c,d;n)\) and \(t(a,b,c,d;n)\) and (\(p,k\))-parametrization of theta functions
• Congruences modulo 16, 32, and 64 for Andrews's singular overpartitions
• Some relations between $t(a,b,c,d;n)$ and $N(a,b,c,d;n)$
• On the number of representations of n as a linear combination of four triangular numbers II
• Binary quadratic forms and sums of triangular numbers
• SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS INDUCED BY PARTITIONS OF 8
• Cubic Analogues of the Jacobian Theta Function θ(z, q)
• A GENERAL RELATION BETWEEN SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS

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