Universal Triple Massey Products on Elliptic Curves and Hecke’s Indefinite Theta Series
نویسنده
چکیده
Generalizing [10] we express universal triple Massey products between line bundles on elliptic curves in terms of Hecke’s indefinite theta series. We show that all Hecke’s indefinite theta series arise in this way. 2000 Math. Subj. Class. Primary 14H52; Secondary 55S30.
منابع مشابه
2 1 A ug 2 00 4 UNIVERSAL TRIPLE MASSEY PRODUCTS ON ELLIPTIC CURVES AND HECKE ’ S INDEFINITE THETA SERIES
Generalizing [11] we express universal triple Massey products between line bundles on elliptic curves in terms of Hecke's indefinite theta series. We show that all Hecke's indefinite theta series arise in this way.
متن کاملNew Look at Hecke’s Indefinite Theta Series
where Q is an indefinite quadratic form on Z, f(m,n) is a doubly periodic function on Z such that the sums of f(m,n)q over all vertical and all horizontal lines in Z vanish. Some of these series appeared as coefficients in univalued triple Massey products on elliptic curves computed via homological mirror symmetry in [3]. In particular, in this context the condition of vanishing of sums over ve...
متن کاملA New Look at Hecke’s Indefinite Theta Series
where Q is an indefinite quadratic form on Z, f(m,n) is a doubly periodic function on Z such that the sums of f(m,n)q over all vertical and all horizontal lines in Z vanish. Some of these series appeared as coefficients in univalued triple Massey products on elliptic curves computed via homological mirror symmetry in [3]. In particular, in this context the condition of vanishing of sums over ve...
متن کاملIndefinite Theta Series of Signature (1, 1) from the Point of View of Homological Mirror Symmetry
We apply the homological mirror symmetry for elliptic curves to the study of indefinite theta series. We prove that every such series corresponding to a quadratic form of signature (1,1) can be expressed in terms of theta series associated with split quadratic forms and the usual theta series. We also show that indefinite theta series corresponding to univalued Massey products between line bund...
متن کاملMassey and Fukaya Products on Elliptic Curves
This note is a continuation of [6]. Its goal is to show that some higher Massey products on elliptic curve can be computed as higher compositions in Fukaya category of the dual symplectic torus in accordance with the homological mirror conjecture of M. Kontsevich [4]. Namely, we consider triple Massey products of very simple type which are uniquely defined, compute them in terms of theta-functi...
متن کامل