An identity of Ramanujan and the representation of integers as sums of triangular numbers

DOI10.1023/B:RAMA.0000012425.42327.aezbMath1041.11028OpenAlexW2035579015WikidataQ56169287 ScholiaQ56169287MaRDI QIDQ1430276

Zhi-Guo Liu

Publication date: 27 May 2004

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/b:rama.0000012425.42327.ae

zbMATH Keywords

Jacobi's identityLambert seriesmodular formstheta functionselliptic functionstriangular numbersRamanujan \(\tau(n)\)-function

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Theta series; Weil representation; theta correspondences (11F27) Holomorphic modular forms of integral weight (11F11) Automorphic forms, one variable (11F12) Elliptic functions and integrals (33E05)

Related Items (8)

More infinite families of congruences modulo 5 for broken 2-diamond partitions ⋮ An addition formula for the Jacobian theta function and its applications ⋮ A three-term theta function identity and its applications ⋮ Proof for a \(q\)-trigonometric identity of Gosper ⋮ On the representation of integers as sums of a class of triangular numbers ⋮ On series identities of Gosper and integrals of Ramanujan theta function 𝜓(𝑞) ⋮ On decomposition of \(\theta_2^{2n}(\tau)\) as the sum of Eisenstein series and cusp forms ⋮ ON THE q-DERIVATIVE AND q-SERIES EXPANSIONS

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