K. Saito's Conjecture for nonnegative eta products and analogous results for other infinite products

DOI10.1016/j.jnt.2007.02.002zbMath1143.05008arXivmath/0702027OpenAlexW2106846946WikidataQ123259260 ScholiaQ123259260MaRDI QIDQ927724

Alexander Berkovich, Frank G. Garvan

Publication date: 9 June 2008

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

Full work available at URL: https://arxiv.org/abs/math/0702027

zbMATH Keywords

Dedekind's eta functionquintuple product identity\(p\)-coresinfinite products with nonnegative coefficientsK. Saito's Conjecturemultidimensional theta function

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65) Theta series; Weil representation; theta correspondences (11F27) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Fourier coefficients of automorphic forms (11F30) Dedekind eta function, Dedekind sums (11F20)

Related Items (5)

On certain weighted 7-colored partitions ⋮ Combinatorial interpretations of Ramanujan's tau function ⋮ The spt-crank for overpartitions ⋮ On a certain vector crank modulo 7 ⋮ Non-negativity of the Fourier coefficients of eta products associated to regular systems of weights

Cites Work

• Modular forms and representations of symmetric groups
• Inequalities for the crank
• Duality for regular systems of weights
• The BG-rank of a partition and its applications
• Affine root systems and Dedekind's \(\eta\)-function
• Positivity of eta products -- a certain case of K. Saito's conjecture
• Cranks and t-cores
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• Cubic Analogues of the Jacobian Theta Function θ(z, q)
• Defect zero blocks for finite simple groups
• On the Andrews-Stanley refinement of Ramanujan’s partition congruence modulo 5 and generalizations
• Modular representations of symmetric groups
• Some Properties of Partitions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: K. Saito's Conjecture for nonnegative eta products and analogous results for other infinite products