On the number of representations of n as a linear combination of four triangular numbers II

DOI10.1142/S1793042117500300zbMath1380.33012arXiv1511.00478OpenAlexW4232962141WikidataQ114072001 ScholiaQ114072001MaRDI QIDQ2969715

Zhi-Hong Sun, Min Wang

Publication date: 23 March 2017

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

Full work available at URL: https://arxiv.org/abs/1511.00478

zbMATH Keywords

theta functionpower series expansionnumber representationtriangular number

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Power series (including lacunary series) in one complex variable (30B10) Other functions defined by series and integrals (33E20) Representation problems (11D85)

Related Items

Automatic proofs of some conjectures of Sun on the relations between sums of squares and sums of triangular numbers ⋮ Quartic congruences and eta products ⋮ Ramanujan’s theta functions and sums of triangular numbers ⋮ Proofs of some conjectures of Sun on the relations between sums of squares and sums of triangular numbers ⋮ 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 ⋮ Proofs of some conjectures of Z.-H. Sun on relations between sums of squares and sums of triangular numbers ⋮ The number of representations of n as a linear combination of triangular numbers ⋮ Relations among representations of integers by certain quadratic forms

Cites Work

• Representations by quaternary quadratic forms whose coefficients are 1, 4, 9 and 36
• On the number of representations of n as a linear combination of four triangular numbers
• SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS INDUCED BY PARTITIONS OF 8
• THETA FUNCTION IDENTITIES AND REPRESENTATIONS BY CERTAIN QUATERNARY QUADRATIC FORMS
• THE NUMBER OF REPRESENTATIONS OF A POSITIVE INTEGER BY CERTAIN QUATERNARY QUADRATIC FORMS
• CONGRUENCES CONCERNING LEGENDRE POLYNOMIALS III
• Nineteen quaternary quadratic forms
• Representations by quaternary quadratic forms whose coefficients are 1, 3 and 9
• Multiplicative 𝜂-quotients
• A GENERAL RELATION BETWEEN SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS
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