Some relations between $t(a,b,c,d;n)$ and $N(a,b,c,d;n)$

DOI10.4064/AA8418-5-2016zbMath1402.11055arXiv1511.06177OpenAlexW2964179594MaRDI QIDQ2833600

Zhi-Hong Sun

Publication date: 18 November 2016

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.06177

zbMATH Keywords

theta functionpower series expansiontriangular number

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Theta series; Weil representation; theta correspondences (11F27) Other functions defined by series and integrals (33E20) Representation problems (11D85)

Related Items (13)

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 ⋮ Sums of triangular numbers and sums of squares ⋮ Automatic proofs of some conjectures of Sun on the relations between sums of squares and sums of triangular numbers ⋮ Generalizations of some conjectures of Sun on the relations between \(N(a,b,c,d;n)\) and \(T(a,b,c,d;n)\) ⋮ 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 ⋮ The number of representations by a ternary sum 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
• ON THE QUATERNARY FORMS x²+y²+2z²+3t², x²+2y²+2z²+6t², x²+3y²+3z²+6t² AND 2x²+3y²+6z²+6t²
• 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
• Nineteen quaternary quadratic forms
• Representations by quaternary quadratic forms whose coefficients are 1, 3 and 9
• A GENERAL RELATION BETWEEN SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS
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