Special L-values and Selmer groups of Siegel modular forms of genus 2

2018/11/05 by Zhang, Xiaoyu
#11F27 #11F33 #11F46 #11F67 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1811.02031

Abstract

Let p be an odd prime, N a square-free odd positive integer prime to p, π a p-ordinary cohomological irreducible cuspidal automorphic representation of GSp₄(\mathbbA_ℚ) of principal level N and Iwahori level at p. Using a p-integral version of Rallis inner product formula and modularity theorems for GSp_4/ℚ and U_4/ℚ, we establish an identity between the p-part of the critical value at 1 of the degree 5 L-function of π twisted by the non-trivial quadratic Dirichlet character ξ associated to the extension ℚ(√(-N))/ℚ and the p-part of the Selmer group of the degree 5 Galois representation associated to π twisted by ξ, under certain conditions on the residual Galois representation.

Related

• Transfer of Siegel cusp forms of degree 2
• Integral representation and critical L-values for holomorphic forms on GSp_2n × GL₁
• Algebraicity of the near central non-critical value of symmetric fourth L-functions for Hilbert modular forms
• Siegel modular forms of genus 2 attached to elliptic curves
• On special values of standard L-functions of Siegel cusp eigenforms of genus 3