Integer Matrix Exact Covering Systems and Product Identities for Theta Functions
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Publication:3097879
DOI10.1093/imrn/rnq253zbMath1247.33028arXiv1005.5116OpenAlexW1978009149MaRDI QIDQ3097879
Publication date: 10 November 2011
Published in: International Mathematics Research Notices (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1005.5116
theta functionsproducts of theta functionsidentities for two theta functionsinteger matrix exact covering systems
Theta series; Weil representation; theta correspondences (11F27) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)
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On Applications of Roots of Unity to Product Identities ⋮ On rational matrix exact covering systems of \(\mathbb{Z}^n\) and its applications to Ramanujan's forty identities ⋮ Congruences for generalized Frobenius partitions with 6 colors ⋮ Ramanujan-style proof of \(p_{-3}(11n+7) \equiv 0 \pmod{11}\) ⋮ Further results on Vanishing Coefficients in infinite products of the form (qb,qp−b;qp)∞3(qjb,q2p−jb;q2p)∞ ⋮ Generalized Frobenius partitions, Motzkin paths, and Jacobi forms ⋮ Infinite families of arithmetic identities for self-conjugate 5-cores and 7-cores ⋮ Generalized Frobenius partitions with 6 colors ⋮ Vanishing coefficients in quotients of theta functions with odd moduli ⋮ Vanishing coefficients in three families of products of theta functions ⋮ The method of constant terms and \(k\)-colored generalized Frobenius partitions ⋮ Stanley's Lemma and Multiple Theta Functions ⋮ Vanishing coefficients in three families of products of theta functions. II ⋮ The \(t\)-coefficient method. III: A general series expansion for the product of theta functions with different bases and its applications. ⋮ Modular forms and $k$-colored generalized Frobenius partitions ⋮ On Somos' dissection identities ⋮ Congruences for generalized Frobenius partitions with 4 colors ⋮ New infinite \(q\)-product expansions with vanishing coefficients ⋮ A generalization of Schröter's formula ⋮ Some extensions for Ramanujan's circular summation formulas and applications ⋮ On conjectures of Koike and Somos for modular identities for the Rogers–Ramanujan functions ⋮ Vanishing coefficients in two families of quotients of theta functions ⋮ On generalized Schur’s partitions
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