The number of representations of n as a linear combination of triangular numbers

DOI10.1142/S1793042119500660zbMath1435.11074OpenAlexW4255293475WikidataQ114071970 ScholiaQ114071970MaRDI QIDQ5223030

Zhi-Hong Sun

Publication date: 4 July 2019

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

Full work available at URL: https://doi.org/10.1142/s1793042119500660

zbMATH Keywords

quadratic formtheta functionnumber of representationstriangular numbers

Mathematics Subject Classification ID

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

Related Items (9)

On conjectures of Z.-H. Sun ⋮ Proofs of some conjectures of Sun on the relations between \(T(a, b, c, d; n)\) and \(N(a, b, c, d; n)\) ⋮ Unnamed Item ⋮ Automatic proofs of some conjectures of Sun on the relations between sums of squares and sums of triangular numbers ⋮ Quartic congruences and eta products ⋮ Unnamed Item ⋮ Proofs of some conjectures of Sun on representations by linear combinations 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

Cites Work

• Unnamed Item
• The relations between \(N(a,b,c,d;n)\) and \(t(a,b,c,d;n)\) and (\(p,k\))-parametrization of theta functions
• 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
• Eta-quotients and elliptic curves
• The Chowla-Selberg formula for genera
• Legendre polynomials and supercongruences
• Ramanujan’s theta functions and sums of triangular numbers
• Nineteen quaternary quadratic forms
• On the number of representations of n by ax²+bxy+cy²
• Multiplicative 𝜂-quotients
• A GENERAL RELATION BETWEEN SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS

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