The number of representations of a positive integer by triangular, square, and decagonal numbers

DOI10.4134/BKMS.b180914zbMath1459.11101OpenAlexW2995766724MaRDI QIDQ5242402

Uha Isnaini, Unnamed Author, Pee Choon Toh

Publication date: 8 November 2019

Full work available at URL: https://opus.lib.uts.edu.au/bitstream/10453/137359/1/THE_NUMBER_OF_REPRESENTATIONS_OF_A_POSITIVE_INTEGER_BY_TRIANGULAR%2c_SQUARE_AND_DECAGONAL_NUMBERS.pdf

zbMATH Keywords

representations by binary quadratic forms

Mathematics Subject Classification ID

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

Cites Work

• On the number of representations of \(n\) by \(ax(x-1)/2+by(y-1)/2\)
• Proof of some conjectures of Melham using Ramanujan's \(_1 \psi_1\) formula
• The power of \(q\). A personal journey
• 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)
• Analogues of Jacobi's Two-Square Theorem: An Informal Account
• Representations of certain binary quadratic forms as Lambert series
• ON REPRESENTATIONS BY FIGURATE NUMBERS: A UNIFORM APPROACH TO THE CONJECTURES OF MELHAM
• Theta series associated with certain positive definite binary quadratic forms
• On the number of representations of n by ax²+bxy+cy²
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