On representations of a number as a sum of three squares

DOI10.1016/S0012-365X(98)00288-XzbMath0946.11010OpenAlexW2121254642MaRDI QIDQ1297434

James A. Sellers, Michael D. Hirschhorn

Publication date: 19 November 2000

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0012-365x(98)00288-x

zbMATH Keywords

generating functionnumber of representationssum of three squaresmodular forms of half-integral weightJacobi's triple product

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Sums of squares and representations by other particular quadratic forms (11E25) Waring's problem and variants (11P05) Forms of half-integer weight; nonholomorphic modular forms (11F37)

Related Items (20)

On the number of primitive representations of integers as sums of squares ⋮ Multiplication theorems for self-conjugate partitions ⋮ Congruences modulo 64 and 1024 for overpartitions ⋮ Unnamed Item ⋮ Arithmetic properties of partition triples with odd parts distinct ⋮ On the Diophantine equation \(n^2 = x^2 +by^2 +cz^2\) ⋮ Infinite families of arithmetic identities for self-conjugate 5-cores and 7-cores ⋮ On the representation numbers of ternary quadratic forms and modular forms of weight \(3/2\) ⋮ On the number of representations of certain integers as sums of 11 or 13 squares. ⋮ Results of Hurwitz type for three squares. ⋮ On Representation of an Integer by X 2 + Y 2 + Z 2 and the Modular Equations of Degree 3 and 5 ⋮ Cooper and Lam's conjecture for generalized Bell ternary quadratic forms ⋮ New congruences modulo 5 and 9 for partitions with odd parts distinct ⋮ Arithmetic properties of overpartition triples ⋮ INFINITE FAMILIES OF ARITHMETIC IDENTITIES FOR 4-CORES ⋮ Proof of a conjecture of Cooper ⋮ INFINITE FAMILIES OF ARITHMETIC IDENTITIES FOR DOUBLED DISTINCT t-CORES FOR t = 3, 4, …, 10 ⋮ SUMS OF SQUARES AND PARTITION CONGRUENCES ⋮ CONGRUENCES MODULO 4 FOR WEIGHT ETA-PRODUCTS ⋮ A new analogue of $t$-core partitions

Cites Work

• Unnamed Item
• Two congruences involving 4-cores
• Some amazing facts about \(4\)-cores
• On representations of a number as a sum of three triangles

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