ON REPRESENTATIONS BY FIGURATE NUMBERS: A UNIFORM APPROACH TO THE CONJECTURES OF MELHAM

DOI10.1142/S1793042113500127zbMath1281.11033OpenAlexW1988920771WikidataQ123114554 ScholiaQ123114554MaRDI QIDQ4923264

Pee Choon Toh

Publication date: 6 June 2013

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

Full work available at URL: https://doi.org/10.1142/s1793042113500127

zbMATH Keywords

Lambert seriesbinary quadratic formssum of squaresfigurate numbers

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) General binary quadratic forms (11E16) Representation problems (11D85)

Related Items (3)

Unnamed Item ⋮ The number of representations of a positive integer by triangular, square, and decagonal numbers ⋮ Proof of some conjectures of Melham using Ramanujan's \(_1 \psi_1\) formula

Cites Work

• Ramanujan's identities and representation of integers by certain binary and quaternary quadratic forms
• On the number of representations of \(n\) by \(ax(x-1)/2+by(y-1)/2\)
• Relations between squares and triangles
• The number of representations of a number by various forms
• Binary quadratic forms and sums of triangular numbers
• On the number of representations of n by ax²+by(y-1)/2, ax²+by(3y-1)/2 and ax(x-1)/2+by(3y-1)/2
• The expansion of ∏_k=1^∞(1-q^ak)(1-q^bk)
• Representations of certain binary quadratic forms as Lambert series
• On the number of representations of n by ax²+bxy+cy²
• A GENERAL RELATION BETWEEN SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS
• Generalized Lambert series identities
• The Number of Representations Function for Binary Quadratic Forms

This page was built for publication: ON REPRESENTATIONS BY FIGURATE NUMBERS: A UNIFORM APPROACH TO THE CONJECTURES OF MELHAM