On the Petersson scalar product of arbitrary modular forms

On Dirichlet Series and Petersson Products for Siegel Modular Forms

— We prove that the Dirichlet series of Rankin–Selberg type associated with any pair of (not necessarily cuspidal) Siegel modular forms of degree n and weight k > n/2 has meromorphic continuation to C. Moreover, we show that the Petersson product of any pair of square–integrable modular forms of weight k > n/2 may be expressed in terms of the residue at s = k of the associated Dirichlet series....

Scalar Product Graphs of Modules

Let R be a commutative ring with identity and M an R-module. The Scalar-Product Graph of M is defined as the graph GR(M) with the vertex set M and two distinct vertices x and y are adjacent if and only if there exist r or s belong to R such that x = ry or y = sx. In this paper , we discuss connectivity and planarity of these graphs and computing diameter and girth of GR(M). Also we show some of...

Product Formulas for Modular Forms on O(2, N)

Modular Forms on

Let k 2 Z and let SL 2 (Z) denote the special linear group SL 2 (Z) = a b c d : a; b; c; d 2 Z and ad bc = 1 : A modular form of weight k is an analytic function f de…ned on the complex upper half plane H = fz 2 C : Im(z) > 0g that transforms under the action of SL 2 (Z) according to the relation [1] f az + b cz + d = (cz + d) k f (z) for all a b c d 2 SL 2 (Z)

survey on the rule of the due & hindering relying on the sheikh ansaris ideas

قاعده مقتضی و مانع در متون فقهی کم و بیش مستند احکام قرار گرفته و مورد مناقشه فقهاء و اصولیین می باشد و مشهور معتقند مقتضی و مانع، قاعده نیست بلکه یکی از مسائل ذیل استصحاب است لذا نگارنده بر آن شد تا پیرامون این قاعده پژوهش جامعی انجام دهد. به عقیده ما مقتضی دارای حیثیت مستقلی است و هر گاه می گوییم مقتضی احراز شد یعنی با ماهیت مستقل خودش محرز گشته و قطعا اقتضاء خود را خواهد داشت مانند نکاح که ...