On conjectures of Z.-H. Sun

DOI10.1007/s00025-022-01640-5zbMath1483.11069OpenAlexW4221080063WikidataQ122940688 ScholiaQ122940688MaRDI QIDQ2124526

Dongxi Ye, Qinghai Jiang, Dieqi Gu, Tinghao Huang, Yi-Hao Ding

Publication date: 11 April 2022

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-022-01640-5

zbMATH Keywords

quadratic formmodular formtriangular number

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Modular and automorphic functions (11F03) Representation problems (11D85)

Cites Work

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• Proofs of some conjectures of Sun on the relations between \(N(a,b,c,d;n)\) and \(t(a,b,c,d;n)\)
• 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
• Generalizations of some conjectures of Sun on the relations between \(N(a,b,c,d;n)\) and \(T(a,b,c,d;n)\)
• Some relations between $t(a,b,c,d;n)$ and $N(a,b,c,d;n)$
• Ramanujan's Theta Functions
• Über einige Anwendungen Dedekindscher Summen.
• TRANSFORMATION FORMULAS FOR THE NUMBER OF REPRESENTATIONS OF BY LINEAR COMBINATIONS OF FOUR TRIANGULAR NUMBERS
• Ramanujan’s theta function identities and the relations between sums of squares and sums of triangular numbers
• The number of representations by a ternary sum of triangular numbers
• 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

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