Shih-Yu Chen

activity

20182026

most citedGamma factors for the Asai cube representation

9 citations · 28 across the 17 of their papers we have counts for

collaborators

17 papers

math.NT2026

Betti-Whittaker periods under duality: variations and applications

Giancarlo Castellano, Shih-Yu Chen, Nasit Darshan +1

One of the authors (Chen) had previously proved a result on the behavior of Betti-Whittaker periods under duality for cohomological cuspidal automorphic representations of ${\rm GL…

math.NT2026

Whittaker functions on $GL_{n}$ via theta lifting

Shih-Yu Chen, Yao Cheng

In the literature, two main approaches have been used to establish explicit formulas or propagation formulas for Whittaker functions over Archimedean local fields: one based on Jac…

math.NT2025

Algebraicity of adjoint $L$ -functions for quasi-split groups

Shih-Yu Chen

For a globally generic cuspidal automorphic representation $Π$ of a quasi-split reductive group $G$ over $Q$ , E. Lapid and Z. Mao proposed a conjecture on the decomp…

math.NT2023★ 1 cited

Period relations between the Betti-Whittaker periods for $GL_{n}$ under duality

Shih-Yu Chen

In this paper, under some regularity conditions, we prove a period relation between the Betti--Whittaker periods associated to a regular algebraic cuspidal automorphic representati…

math.NT2022

Algebraicity of ratios of Rankin-Selberg $L$ -functions and applications to Deligne's conjecture

Shih-Yu Chen

In this paper, we prove Deligne's conjecture on the algebraicity of the critical values of symmetric power $L$ -functions associated with modular forms of weight at least 5. We also…

math.NT2021

On Deligne's conjecture for symmetric fifth $L$ -functions of modular forms

Shih-Yu Chen

We prove Deligne's conjecture for symmetric fifth $L$ -functions of elliptic newforms of weight greater than $5$ . As a consequence, we establish period relations between motivic per…

math.NT2021

On Deligne's conjecture for symmetric sixth $L$ -functions of Hilbert modular forms

Shih-Yu Chen

In this paper, we prove Deligne's conjecture for symmetric sixth $L$ -functions of Hilbert modular forms. We extend the result of Morimoto based on a different approach. We define a…

math.NT2021

Algebraicity of critical values of triple product $L$ -functions in the balanced case

Shih-Yu Chen

The algebraicity of critical values of triple product $L$ -functions in the balanced case was proved by Garrett and Harris, under the assumption that the critical points are on the…

math.NT2021★ 1 cited

Algebraicity of critical values of adjoint $L$ -functions for $GSp_{4}$

Shih-Yu Chen

We prove an algebraicity result for certain critical value of adjoint $L$ -functions for $GSp_{4}$ over a totally real number field in terms of the Petersson norm of normalized…

math.NT2021

On Deligne's conjecture for symmetric fourth $L$ -functions of Hilbert modular forms

Shih-Yu Chen

We prove an automorphic analogue of Deligne's conjecture for symmetric fourth $L$ -functions of Hilbert modular forms. We extend the result of Morimoto based on generalization and r…

math.NT2020★ 1 cited

Algebraicity of the near central non-critical value of symmetric fourth $L$ -functions for Hilbert modular forms

Shih-Yu Chen

Let $Π$ be a cohomological irreducible cuspidal automorphic representation of $GL_{2} (A_{F})$ with central character $ω_{Π}$ over a totally real…

math.NT2020

Algebraicity of the central critical values of twisted triple product $L$ -functions

Shih-Yu Chen

We study the algebraicity of the central critical values of twisted triple product $L$ -functions associated to motivic Hilbert cusp forms over a totally real étale cubic algebra in…

math.NT2019★ 9 cited

Gamma factors for the Asai cube representation

Shih-Yu Chen

We prove an equality between the gamma factors for the Asai cube representation of $R_{E / F} GL_{2}$ defined by the Weil $-$ Deligne representations and the local zeta integr…

math.NT2019★ 4 cited

On Petersson norms of generic cusp forms and special values of adjoint $L$ -functions for $GSp_{4}$

Shih-Yu Chen, Atsushi Ichino

We prove an explicit formula for the Petersson norms of some normalized generic cuspidal newforms on $GSp_{4}$ whose archimedean components belong to either discrete series rep…

math.NT2018★ 3 cited

Gamma factors for Asai representations of $GL_{2}$

Shih-Yu Chen, Yao Cheng, Isao Ishikawa

Let $E$ be a quadratic semisimple extension of a local field $F$ of characteristic zero. We determine explicit relation between gamma factors for Asai representations of $R_{E/F}{\…

math.NT2018★ 4 cited

On Deligne's conjecture for certain automorphic $L$ -functions for $GL (3) \times GL (2)$

Shih-Yu Chen, Yao Cheng

We prove Deligne's conjecture for central critical values of certain automorphic $L$ -functions for $GL (3) \times GL (2)$ . The proof is base on rationality results for cen…

math.NT2018★ 5 cited

Pullback formulae for nearly holomorphic Saito-Kurokawa lifts

Shih-Yu Chen

We give explicit pullback formulae for nearly holomorphic Saito-Kurokawa lifts restrict to product of upper half-plane against with product of elliptic modular forms. We generalize…

Betti-Whittaker periods under duality: variations and applications

Whittaker functions on GLn​ via theta lifting

Algebraicity of adjoint L-functions for quasi-split groups

Period relations between the Betti-Whittaker periods for GLn​ under duality

Algebraicity of ratios of Rankin-Selberg L-functions and applications to Deligne's conjecture

On Deligne's conjecture for symmetric fifth L-functions of modular forms

On Deligne's conjecture for symmetric sixth L-functions of Hilbert modular forms

Algebraicity of critical values of triple product L-functions in the balanced case

Algebraicity of critical values of adjoint L-functions for GSp4​

On Deligne's conjecture for symmetric fourth L-functions of Hilbert modular forms

Algebraicity of the near central non-critical value of symmetric fourth L-functions for Hilbert modular forms

Algebraicity of the central critical values of twisted triple product L-functions

Gamma factors for the Asai cube representation

On Petersson norms of generic cusp forms and special values of adjoint L-functions for GSp4​

Gamma factors for Asai representations of GL2​

On Deligne's conjecture for certain automorphic L-functions for GL(3)×GL(2)

Pullback formulae for nearly holomorphic Saito-Kurokawa lifts

Whittaker functions on $GL_{n}$ via theta lifting

Algebraicity of adjoint $L$ -functions for quasi-split groups

Period relations between the Betti-Whittaker periods for $GL_{n}$ under duality

Algebraicity of ratios of Rankin-Selberg $L$ -functions and applications to Deligne's conjecture

On Deligne's conjecture for symmetric fifth $L$ -functions of modular forms

On Deligne's conjecture for symmetric sixth $L$ -functions of Hilbert modular forms

Algebraicity of critical values of triple product $L$ -functions in the balanced case

Algebraicity of critical values of adjoint $L$ -functions for $GSp_{4}$

On Deligne's conjecture for symmetric fourth $L$ -functions of Hilbert modular forms

Algebraicity of the near central non-critical value of symmetric fourth $L$ -functions for Hilbert modular forms

Algebraicity of the central critical values of twisted triple product $L$ -functions

On Petersson norms of generic cusp forms and special values of adjoint $L$ -functions for $GSp_{4}$

Gamma factors for Asai representations of $GL_{2}$

On Deligne's conjecture for certain automorphic $L$ -functions for $GL (3) \times GL (2)$