scholarly journals Algebraicity of special L-values attached to Siegel–Jacobi modular forms

2020 ◽  
Author(s):  
Thanasis Bouganis ◽  
Jolanta Marzec
Keyword(s):  
Exponential Type ◽  
Modular Forms ◽  
Poincaré Series ◽  
Poincare Series ◽  
Jacobi Group ◽  
Doubling Method ◽  
Holomorphic Projection

Abstract In this work we obtain algebraicity results on special L-values attached to Siegel–Jacobi modular forms. Our method relies on a generalization of the doubling method to the Jacobi group obtained in our previous work, and on introducing a notion of near holomorphy for Siegel–Jacobi modular forms. Some of our results involve also holomorphic projection, which we obtain by using Siegel–Jacobi Poincaré series of exponential type.

scholarly journals BRANE SUPERPOTENTIAL AND LOCAL CALABI–YAU MANIFOLDS

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2187-2189 ◽  
Author(s):  
ANTONIO RICCO
Keyword(s):  
Type Ii ◽  
Closed Expression ◽  
Complex Submanifolds ◽  
Local Space ◽  
Tubular Neighborhoods ◽  
Holomorphic Projection ◽  
Calabi Yau Manifolds

We briefly report on some recent progresses in the computation of B-brane superpotentials for Type II strings compactified on Calabi–Yau manifolds, obtained by using a paramatrization of tubular neighborhoods of complex submanifolds, also known as local spaces. In particular, we propose a closed expression for the superpotential of a brane on a genus-g curve in a Calabi–Yau threefold for the cases in which there exists a holomorphic projection from the local space around the curve to the curve itself.

scholarly journals ARITHMETIC PROPERTIES OF CERTAIN LEVEL ONE MOCK MODULAR FORMS

2010 ◽  
Vol 06 (01) ◽  
pp. 185-202 ◽  
Author(s):  
MATTHEW BOYLAN
Keyword(s):  
Theta Function ◽  
Modular Forms ◽  
Hecke Operators ◽  
Mock Theta Function ◽  
Maass Forms ◽  
Maass Form ◽  
Arithmetic Properties ◽  
Holomorphic Projection ◽  
Harmonic Weak Maass Form ◽  
Integer Weight

In a recent work, Bringmann and Ono [4] show that Ramanujan's f(q) mock theta function is the holomorphic projection of a harmonic weak Maass form of weight 1/2. In this paper, we extend the work of Ono in [13]. In particular, we study holomorphic projections of certain integer weight harmonic weak Maass forms on SL 2(ℤ) using Hecke operators and the differential theta-operator.

scholarly journals Sturm’s operator for scalar weight in arbitrary genus

2017 ◽  
Vol 13 (10) ◽  
pp. 2677-2686 ◽  
Author(s):  
Kathrin Maurischat
Keyword(s):  
Modular Forms ◽  
Projection Operator ◽  
Siegel Modular Forms ◽  
Arbitrary Genus ◽  
Genus Formula ◽  
Genus Two ◽  
Holomorphic Projection

In contrast to the well-known cases of large weights, Sturm’s operator does not realize the holomorphic projection operator for lower weights. We prove its failure for arbitrary Siegel modular forms of genus [Formula: see text] and scalar weight [Formula: see text]. This generalizes a result for genus two in [K. Maurischat and R. Weissauer, Phantom holomorphic projections arising from Sturm’s formula, preprint (2016)].

Derivative of the Analytic Kernel

2012 ◽  
Author(s):  
Xinyi Yuan ◽  
Shou-Wu Zhang ◽  
Wei Zhang
Keyword(s):  
Explicit Formula ◽  
General Formula ◽  
Kernel Function ◽  
Schwartz Function ◽  
Explicit Result ◽  
Analytic Kernel ◽  
Holomorphic Projection ◽  
Period Integral ◽  
Local Term

This chapter computes the derivative of the analytic kernel. It first decomposes the kernel function into a sum of infinitely many local terms indexed by places v of Fnonsplit in E. Each local term is a period integral of some kernel function. The chapter then considers the v-part for non-archimedean v. An explicit formula is given in the unramified case, and an approximation is presented in the ramified case assuming the Schwartz function is degenerate. An explicit result of the v-part for archimedean v is also introduced. The chapter proceeds by reviewing a general formula of holomorphic projection, and estimates the growth of the kernel function in order to apply the formula. It also computes the holomorphic projection of the analytic kernel function and concludes with a discussion of the holomorphic kernel function.

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