Zagier Duality for the Exponents of Borcherds Products for Hilbert Modular Forms
نویسنده
چکیده
A certain sequence of weight 1/2 modular forms arises in the theory of Borcherds products for modular forms for SL2(Z). Zagier proved a family of identities between the coefficients of these weight 1/2 forms and a similar sequence of weight 3/2 modular forms, which interpolate traces of singular moduli. We obtain the analogous results for modular forms arising from Borcherds products for Hilbert modular forms.
منابع مشابه
Congruence Properties of Borcherds Product Exponents
In his striking 1995 paper, Borcherds [2] found an infinite product expansion for certain modular forms with CM divisors. In particular, this applies to the Hilbert class polynomial of discriminant −d evaluated at the modular j-function. Among a number of powerful generalizations of Borcherds’ work, Zagier made an analogous statement for twisted versions of this polynomial. He proves that the e...
متن کاملBorcherds products and arithmetic intersection theory on Hilbert modular surfaces
We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight two. Moreover, we determine the arithmetic selfintersection number of the line bundle of modular forms equipped with its Petersson metric on a regular model of a Hilbert modular surface, and study Falt...
متن کاملOn duality of modular G-Riesz bases and G-Riesz bases in Hilbert C*-modules
In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...
متن کاملNotes for a course given at the Second EU/US Summer School on Automorphic Forms on SINGULAR MODULI AND MODULAR FORMS
Singular moduli are the values of the modular j-function at the points in the upper halfplane that satisfy a quadratic equation. These values have been studied by number theorists since the 19 century. They are algebraic and generate class fields of imaginary quadratic fields. Both their norms and traces are integers. The work of Gross and Zagier in the 1980s gave explicit factorizations of the...
متن کاملThe Borcherds-Zagier Isomorphism and a p-Adic Version of the Kohnen-Shimura Map
Let M be the space of even integer weight meromorphic modular forms on SL2(Z) with integer coefficients, leading coefficient equal to one, and whose zeros and poles are supported at cusps and imaginary quadratic irrationals. If r ≥ 0 is an integer, let M+r+1/2(Γ0(4)) be the space of modular forms of half-integral weight r + 1/2with respect to Γ0(4) which satisfy Kohnen’s plus-condition and whos...
متن کامل