Young-Sung Cho

Let $M$ be a squarefree positive integer and $P$ a prime number coprime to $M$ such that $P \sim M^{\eta}$ with $0 < \eta < 2/5$. We simplify the proof of subconvexity bounds for $L(\frac{1]{2}, f \otimes \chi)$ when $f$ is a primitive holomorphic cusp form of level $P$ and $\chi$ is a primitive Dirichlet character modulo $M$. These bounds are attained through an unamplified second moment method using a modified version of the delta method due to R. Munshi. The technique is similar to that

Let π be an irreducible admissible (complex) representation of G L ( 2 ) over a non-Archimedean characteristic zero local field with odd residual characteristic. In this paper, we prove the equality between the local symmetric square L-function associated to π arising from integral representations and the corresponding Artin L-function for its Langlands parameter through the local Langlands correspondence. With this in hand, we show the stability of local symmetric γ-factors attached to π under

Abstract By applying the formula for essential Whittaker functions established by Matringe and Miyauchi, we study five integral representations for irreducible admissible generic representations of GL n over p ‐adic fields. In each case, we show that the integrals achieve local formal L ‐functions defined by Langlands parameters, when the test vector is associated to the new form. We give the relation between local periods involving essential Whittaker functions and special values of formal L ‐f

Let $F$ be a non-archimedean local field of odd characteristic $p > 0$. In this paper, we consider local exterior square $L$-functions $L(s,\pi,\wedge^2)$, Bump-Friedberg $L$-functions $L(s,\pi,BF)$, and Asai $L$-functions $L(s,\pi,As)$ of an irreducible admissible representation $\pi$ of $GL_m(F)$. In particular, we establish that those $L$-functions, via the theory of integral representations, are equal to their corresponding Artin $L$-functions $L(s,\wedge^2(\phi(\pi)))$, $L(s+1/2,\phi(\pi))L

Abstract In this article, we revisit Rankin–Selberg integrals established by Jacquet, Piatetski-Shapiro and Shalika. We prove the equality of Rankin–Selberg local factors defined with Schwartz–Bruhat functions and the factors attached to good sections, introduced by Piatetski-Shapiro and Rallis. Moreover, we propose a notion of exceptional poles in the framework of good sections. For cases of Rankin–Selberg, Asai and exterior square L -functions, the exceptional poles are consistent with well-kn

We compute the local coefficient attached to a pair <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis pi 1 comma pi 2 right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi> π </mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi> π </mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="app

A purely local approach has been developed by Krishnamurthy and Kutzko to compute the Langlands–Shahidi local coefficients for ${\rm SL}(2)$ via types and covers à la Bushnell–Kutzko. In this paper, we extend their method to the non-split case and complet

We prove that for any pair of irreducible principal series representations $(π_1,π_2)$ of $\operatorname{GL}_n(\mathbb{R})$ in general position, the notions of exceptional pole of type 1 and type 2 coincide. Using this identification, we express the Rankin--Selberg $L$-function $L(s,π_1\timesπ_2)$ in terms of the exceptional $L$-factors attached to the irreducible constituents of the derivatives of $π_1$ and $π_2$.

Let $F$ be a non-archimedean local field of odd characteristic $p &gt; 0$. In this paper, we consider local exterior square $L$-functions $L(s,π,\wedge^2)$, Bump-Friedberg $L$-functions $L(s,π,BF)$, and Asai $L$-functions $L(s,π,As)$ of an irreducible admissible representation $π$ of $GL_m(F)$. In particular, we establish that those $L$-functions, via the theory of integral representations, are equal to their corresponding Artin $L$-functions $L(s,\wedge^2(ϕ(π)))$, $L(s+1/2,ϕ(π))L(s,\wedge^2(ϕ(π

Let [Formula: see text] be a non-archimedean local field of characteristic not equal to [Formula: see text] and let [Formula: see text] be a quadratic algebra. We prove the stability of local factors attached to irreducible admissible (complex) representations of [Formula: see text] via the Rankin–Selberg method under highly ramified twists. This includes both the Asai as well as the Rankin–Selberg local factors attached to pairs. Our method relies on expressing the gamma factor as a Mellin tran

We prove that for any pair of irreducible principal series representations $(π_1,π_2)$ of $\operatorname{GL}_n(\mathbb{R})$ in general position, the notions of exceptional pole of type 1 and type 2 coincide. Using this identification, we express the Rankin--Selberg $L$-function $L(s,π_1\timesπ_2)$ in terms of the exceptional $L$-factors attached to the irreducible constituents of the derivatives of $π_1$ and $π_2$.

A purely local approach has been developed by Krishnamurthy and Kutzko to compute Langlands-Shahidi local coefficient for ${\rm SL}(2)$ via types and covers à la Bushnell-Kutzko. In this paper, we extend their method to the non-split case and complete their project. We also study the algebraic structure of Gelfand-Graev representations, which generalizes the results of Chan-Savin and Mishra-Pattanayak to ${\rm SL}(2)$ over non-archimidean local fields without any restriction on the characteristi

Let $π$ be an irreducible admissible representation of $GL_m(F)$, where $F$ is a non-archimedean local field of characteristic zero. We follow the method developed by Cogdell and Piatetski-Shapiro to complete the computation of the local exterior square $L$-function $L(s,π,\wedge^2)$ in terms of $L$-functions of supercuspidal representations via an integral representation established by Jacquet and Shalika in $1990$. We analyze the local exterior square $L$-functions via exceptional poles and Be