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

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 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

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

We study four sums including the Jacquet--Piatetski-Shapiro--Shalika, Flicker, Bump--Friedberg, and Jacquet--Shalika sums associated to irreducible cuspidal representations of general linear groups over finite fields. By computing explicitly, we relate Asai and Bump--Friedberg gamma factors over finite fields to those over nonarchimedean local fields through level zero supercuspidal representation. Via Deligne--Kazhdan close field theory, we prove that exterior square and Bump--Friedberg gamma f

We compute the local coefficient attached to a pair $(π_1,π_2)$ of supercuspidal (complex) representations of the general linear group using the theory of types and covers à la Bushnell-Kutzko. In the process, we obtain another proof of a well-known formula of Shahidi for the corresponding Plancherel constant. The approach taken here can be adapted to other situations of arithmetic interest within the context of the Langlands-Shahidi method, particularly, to that of a Siegel Levi subgroup inside

ABSTRACT Let F be a non-archimedean local field of characteristic different from 2 and G be either an odd special orthogonal group ${\rm SO}_{2r+1}(F)$ or a symplectic group ${\rm Sp}_{2r}(F)$. In this paper, we establish the local converse theorem for G. Namely, for given two irreducible admissible generic representations of G with the same central character, if they have the same local gamma factors twisted by irreducible supercuspidal representations of ${\rm GL}_n(F)$ for all $1 \le n \le r$

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

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