arXiv subjects
Publications and source records attributed to Yubo Jin.
We explicit calculate the archimedean modular symbol for Rankin-Selberg convolutions of $\mathrm{GL}_n(\mathbb{C})\times\mathrm{GL}_n(\mathbb{C})$ and $\mathrm{GL}_n(\mathbb{C})\times\mathrm{GL}_{n+1}(\mathbb{C})$, for all generic cohomological representations.
We define Betti-Whittaker periods for a broad class of cohomological automorphic representations and establish a relation between the periods associated with these representations and their contragredients. This extends a result of Shih-Yu Chen for certain cuspidal automorphic representations.
This paper provides a proof of Deligne's conjecture for critical values of Hecke L-functions following a strategy originated by Harder and Schappacher.
Using the modular symbol approach, we prove the rationality and period relations for certain critical values of Rankin-Selberg L-functions for $\mathrm{GL}(n)\times\mathrm{GL}(n)$ over any number field that contains a CM field.
In this paper, we study the Eisenstein cohomology coming from Eisenstein series associated to degenerate principal series representations and prove certain rationality result.
We formulate and prove the archimedean period relations for Rankin-Selberg convolutions of $\text{GL}(n)\times \text{GL}(n)$ and $\text{GL}(n)\times \text{GL}(n-1)$, for all generic cohomological representations. As a consequence, we prove the non-vanishing of the archimedean modular symbols. This extends the earlier results in [LLS24] for essentially tempered representations of $\text{GL}(n)\times\text{GL}(n-1)$.
In this article, we give a cohomological interpretation of (a special case of) the integrals constructed by the second named author and Q. Zhang \cite{YanZhang2023} which represent the product of Rankin-Selberg $L$-functions of $\mathrm{GL}_n\times\mathrm{GL}_m$ and $\mathrm{GL}_n\times\mathrm{GL}_{n-m-1}$ for $m<n$. As an application, we prove an algebraicity result for the special values of certain $L$-functions. This work is a generalization of the algebraicity result of Raghuram for $\mathrm{GL}_n\times\mathrm{GL}_{n-1}$ \cite{Raghuram2010} in the special case $m=n-1$, and the results of Mahnkopf \cite{Mahnkopf1998, Mahnkopf2005} in the special case $m=n-2$.
In this note, we study the special values for zeta functions of totally real fields using the Shintani's cone decomposition. We prove certain congruence between the special values for zeta functions under the prime degree field extension. This congruence implies the `torsion congruence' proved by Ritter-Weiss which is crucial in the proof of the noncommutative Iwasawa main conjecture for totally real fields.
In this paper, we calculate the ramified local integrals in the doubling method and present an integral representation of standard $L$-functions for classical groups. We explicitly construct local sections of Eisenstein series such that the local ramified integrals represent certain ramified $L$-factors. As an application, we prove algebraicity of special $L$-values and construct $p$-adic $L$-functions for symplectic, unitary, quaternionic unitary and quaternionic orthogonal groups.
Let $n$ and $k$ be positive integers such that $n$ is even. We derive new global integrals for $\mathrm{Sp}_{2n}\times\mathrm{GL}_k$ from the generalized doubling method of Cai, Friedberg, Ginzburg and Kaplan, following a strategy and extending a previous result of Ginzburg and Soudry on the case $n=k=2$. We show that these new integrals unfold to non-unique models on $\mathrm{Sp}_{2n}$. Using the New Way method of Piatetski-Shapiro and Rallis, we show that these new global integrals represent the $L$-functions for $\mathrm{Sp}_{2n}\times\mathrm{GL}_k$, generalizing a previous result of the second-named author on $\mathrm{Sp}_{4}\times\mathrm{GL}_2$ and a previous work of Piatetski-Shapiro and Rallis on $\mathrm{Sp}_{2n}\times\mathrm{GL}_1$.
The purpose of this paper is to study the special values of the standard $L$-functions for quaternionic modular forms using the doubling method. We obtain an integral representation for the $L$-function twisted by a character and construct the $p$-adic measure interpolating certain special $L$-values.
In this paper we prove the algebraicity of some L-values attached to quaternionic modular forms. We follow the rather well established path of the doubling method. Our main contribution is that we include the case where the corresponding symmetric space is of non-tube type. We make various aspects very explicit such as, the doubling embedding, coset decomposition, and the definition of algebraicity of modular forms via CM points.