Web8. dec 2024 · Abstract: We prove uniform bounds for the Petersson norm of the cuspidal part of the theta series. This gives an improved asymptotic formula for the number of representations by a quadratic form. This gives an improved asymptotic formula for the number of representations by a quadratic form. Webforms – Theta series; ... k,m and the Jacobi-Petersson inner product 30 2.6.1. Hecke theory of J k,m 30 2.6.2. The Jacobi-Petersson inner product 34 2.7. Taylor expansions 36 ... Generalized Borcherds Products 291 18.1. The simplest Borcherds products 291 18.2. Twisted Borcherds products 294 18.3. Generalization to the mock modular setting 295
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Web20. nov 2012 · In this paper we study regularized Petersson products between a holomorphic theta series associated to a positive definite binary quadratic form and a … Web(2)The theta lift k maps (parabolic) Poincar e series P k+1 2;‘ to other types of Poincar e series; the functions f k; are sums of the hyperbolic Poincar e series which appeared in … cute bear boy minecraft skin
Expansions at Cusps and Petersson Products in Pari/GP
Webform, the Petersson product is defined as f,g= 1 [SL(2,Z):Γ0[N]] F N fgyk d∗z, where FN is a fundamental domain for H modulo Γ0[N] and d∗z is the invariant measure y−2 dxdy. A classical result is that the above product can be expressed in terms of a certain Dirichlet series. More precisely, Petersson proved in [8] that the Dirichlet ... Web11. apr 2024 · We compute adjoints of higher order Serre derivative maps with respect to the Petersson scalar product. As an application, we obtain certain relations amon ... It is well known that the Eisenstein series \(E_2\) ... M., Zagier, D., A generalized Jacobi theta function and quasimodular forms, The moduli space of curves (Texel Island,: Progr. Math ... Web2. apr 2024 · 3. We know the Poincare series are defined as the following: The m t h Poincare series of weight k for Γ is: P m k ( z) = ∑ ( c, d) = 1 ( c z + d) − k e 2 π i n ( τ z). The definition yields that, via the Petersson inner product, we obtain: f, P m k = c k, m a m, cheap american girl doll clothing