arXiv subjects

Pan Yan

Publications and source records attributed to Pan Yan.

At least 19 recordsLinked to original sources

arXiv2026

Twisted automorphic descent to odd GSpin groups and applications

We establish twisted automorphic descent from $(\mathrm{GL}_{2n}, \mathrm{GSpin}_2^{\delta})$, where $\mathrm{GSpin}_2^{\delta}$ is anisotropic, to the odd $\mathrm{GSpin}$ group $\mathrm{GSpin}^{\delta,\alpha}_{2n+1}$, which may be split or non-split, generalizing a construction of Jiang--Liu--Xu--Zhang. As an application, we give a new explicit construction of the global Jacquet--Langlands correspondence between $\mathrm{GL}_2$ and $D^\times$, where $D$ is a quaternion division algebra over a number field. As another application, we prove a new case of the global Gan--Gross--Prasad conjecture for $(\mathrm{GSpin}_{2n+1}, \mathrm{GSpin}^{\delta}_2)$.

math.NT↗

arXiv2026

Comparative study of equilibrium and non-equilibrium predictions by different models for a hypersonic cone at high-altitude

Targeting a cone with the half-angle as 10-deg at M = 27 and H = 72 km, simulations were conducted comparatively to analyze the predictions by different equilibrium and non-equilibrium gas models. Following validation and grid studies, systematic comparisons on aerodynamic performance, flow structures, and characteristic distributions were performed. The key findings are: (1) While the overall flow structures are broadly similar, discrepancies exist in the features at the base locations, e.g., the diverse high-temperature distributions. Notably, the vibrational temperatures distribute differently under slip and non-slip boundary conditions near the wall; (2) The equilibrium gas model predicts higher drag coefficient, wall heat flux, and skin friction than those of non-equilibrium models. Predictions also vary among the non-equilibrium models themselves. Specifically, compared to the three-temperature model, the one- and two-temperature models predict larger drag coefficients with the relative difference exceeding 5%. Nevertheless, the results from the three-temperature model with and without slip conditions are largely consistent; (3) The disparities between equilibrium and non-equilibrium characteristics are primarily manifested in the shock layer and wake regions. Within these regions, the overall temperature for the equilibrium gas is lower than that for the non-equilibrium cases, while in the latter specific non-equilibrium features are distinctly exhibited, e.g., the translational-rotational temperature is generally higher than that from the one-temperature model, and the vibrational-electronic temperature shows the opposite trend. Notably, in the slip flow within the three-temperature model, the translational-rotational temperature is higher and, particularly, the vibrational temperature is even larger than counterparts of the non-slip flows near the wall and base center line.

physics.flu-dyn↗

arXiv2025

Numerical study of friction reduction and underlying mechanism of air film via parallel and tandem injections on a hypersonic flat plate at high altitude

This study uses numerical simulations to analyze a flat-plate with air films generated via parallel and tandem injections under freestream conditions of Ma=15 at an altitude of H=60km. Simulations are carried out using various mass flow rates and jet spacing, followed by an examination of the effect of the streamwise-to-spanwise aspect ratio of the injection hole. The following key findings are acquired: (1) Under hypersonic and high-altitude conditions, the air injection lifts the incoming flow, producing a pronounced low-speed region near the injection site and over the downstream wall. A plateau appears in the wall-normal distribution of the streamwise velocity, with a value significantly lower than that of its freestream counterpart. This reduces the near-wall velocity gradient, thereby achieving drag reduction. However, the subsequent flow reattachment may lead to localized drag increases; (2) As the mass flow rate of injection increases, the wall-normal extent of the near-wall low-speed layer expands and the film coverage broadens; however, the increased friction limits gains in drag reduction, and greater flow losses are also incurred; (3) Increasing the hole spacing in the parallel injection reduces the penetration height of the film, the spanwise coverage, and the drag reduction efficiency, as well as decreasing the flow losses. In contrast, for the studied tandem injections, no significant differences are observed with analogous spacing variations; (4) Increasing the injection aspect ratio enlarges the spanwise coverage of the low-speed layer, improves the spanwise uniformity of the streamwise velocity distribution, diminishes the friction-increasing zones, and significantly enhances the drag reduction. Notably, the consequences are the inverse of those of the low-speed situation.

physics.flu-dyn↗

arXiv2025

Accuracy analysis and optimization of scale-independent third-order WENO-Z scheme with critical-point accuracy preservation

To address the order degradation at critical points in the WENO3-Z scheme, some improvements have been proposed , but these approaches generally fail to consider the occurrence of critical points at arbitrary positions within grid intervals, resulting in their inability to maintain third-order accuracy when a first-order critical point (CP1) occurs. Also, most previous improved schemes suffer from a relatively large exponent p of the ratio of global to local smoothness indicators, which adversely affects the numerical resolution. Concerning these limitations, introduced here is an accuracy-optimization lemma demonstrating that the accuracy of nonlinear weights can be enhanced providing that smoothness indicators satisfy specific conditions, thereby establishing a methodology for elevating the accuracy of nonlinear weights. Leveraging this lemma, a local smoothness indicator is constructed with error terms achieving second-order in smooth regions and fourth-order at CP1, alongside a global smoothness indicator yielding fourth-order accuracy in smooth regions and fifth-order at CP1, enabling the derivation of new nonlinear weights that meet accuracy requirements even when employing p=1. Furthermore, a resolution-optimization lemma is proposed to analyze the relationship between parameters in local smoothness indicators and resolution. By integrating theoretical analysis with numerical practices, free parameters in non-normalized weights and local smoothness indicators are determined under the balance of numerical resolution and robustness, which leads to the development of WENO3-ZES4, a new WENO3-Z improvement that preserves the optimal order at CP1 especially with p=1. 1D and 2D validating tests show that the new scheme consistently achieves third-order in the case of CP1 regardless of its position and exhibits good resolution as well as preferable robustness.

math.NA↗

arXiv2025

Rankin-Selberg integrals for $\mathrm{GSpin}$ groups with application to the global Gan-Gross-Prasad conjecture

We construct Rankin-Selberg integrals using Bessel models for a product of tensor product partial $L$-functions \begin{equation*} L^S(s,\pi\times\tau_1) L^S(s,\pi\times\tau_2)\cdots L^S(s,\pi\times\tau_r) \end{equation*} where $\pi$ is an irreducible cuspidal automorphic representation of a quasi-split $\mathrm{GSpin}$ group, and $\tau_1, \cdots, \tau_r$ are irreducible unitary cuspidal automorphic representations of $\mathrm{GL}_{k_1}, \cdots, \mathrm{GL}_{k_r}$ respectively. As an application, we prove one direction of the global Gan-Gross-Prasad conjecture for generic representations of quasi-split $\mathrm{GSpin}$ groups.

math.NT↗

arXiv2025

Component groups for non-supercuspidal $L$-parameters for $p$-adic $\mathrm{SL}_3$

We explicitly classify all the component groups associated to the non-supercuspidal, tempered $L$-parameters of $\mathrm{SL}_3(F)$ for a $p$-adic field $F$ of characteristic $0$ by direct case-by-case computations in $\mathrm{PGL}_3(\mathbb{C})$, following earlier work for $\mathrm{SL}_2$ by Labesse-Langlands and Shelstad.

math.RT↗

arXiv2025

Uniqueness of Bessel models for GSpin groups

We prove the uniqueness of general Bessel models for $\mathrm{GSpin}$ groups over a local field of characteristic zero. The proof is to reduce it to the spherical case, which has been proved by Emory and Takeda in the non-archimedean case and by Emory, Kim, and Maiti in the archimedean case.

math.RT↗

arXiv2025

Evolution and sudden change of steady interactions of low enthalpy hypersonic double wedge flows with fore angle

The evolution and sudden change of steady interaction structures is numerically studied with the fore wedge angle theta_1 in a low enthalpy hypersonic double wedge configuration. It particularly focuses on the conditions of Swantek and Austin's experiments where Ma=7, and h_0=2 MJ/kg but with a reduced Reynolds number (Re). The sudden structural change indicates that when theta_1 reaches a critical value, minor angular variations can trigger a discontinuous transformation in flow structures. The analysis is based on the laminar Navier-Stokes equations, using ideal gas and non-equilibrium gas models. Under the condition of Re=1E5/m, detailed numerical simulations are conducted as theta_1 varies over 0 deg-40 deg. This study yields the following findings: (a) The upper and lower boundaries of theta_1 for the onset of unsteady flow are identified. When theta_1 lies outside these boundaries, the flow remains steady. (b) As theta_1 increases, the interaction patterns evolve sequentially, progressing from Type VI through Type VI->V, Type III, Type IV_r, and ultimately to a flow dominated solely by a bow shock. This evolution defines the boundaries between different interaction patterns and provides a comprehensive understanding of their progression with theta_1. Sudden structural changes occur during the transitions from Type III to Type IV_r and from Type IV_r to a bow shock-dominated flow. In addition, a comparative study is performed through shock polar analysis to compare its predictions with computational results. (c) An unconventional reflection pattern of the transmitted shock over the separation zone, called Type III_r, is observed in non-equilibrium gas flows, which differs from classical interaction patterns. (d) The aerodynamic distribution of wall properties under various interactions is obtained, indicating distinct features before and after the sudden structural change.

physics.flu-dyn↗

arXiv2024

Numerical studies on steady interaction of low enthalpy hypersonic double wedge flows using different gas models

Numerical investigations and analyses are carried out particularly on the steady interactions of low enthalpy hypersonic 30-55-deg double wedge configuration at conditions similar to the experimental setup by Swantek & Austin. To achieve a steady solution, Re lower than those in the experiment are used. Three gas models, i.e., the perfect, equilibrium, and non-equilibrium gas models, are used to analyze the difference potentials that arise from the physical model. Grid convergence studies are first conducted at Ma=7 and Re=2.5e5/m. Subsequently, comprehensive numerical studies are carried out on the steady interactions and their evolution at Ma=7 and h0=2.1MJ/kg. Specifically: (a) The upper limits of Re are identified where the flows remain steady, and the corresponding interaction characteristics as well as differences in the three gas models are investigated. Notably, a quasi-normal shock wave is observed within the slip line passage in the case of the perfect gas model. (b) The flow characteristics of the three models, including the interaction pattern, geometric features of triple points, impingements, and separation zone, are studied and compared for Re=(4,3,2)e4/m. Differences primarily emerge between the results of the perfect gas model and the real gas model. Specifically, a transmitted shock reflecting above the separation zone is observed in the case of the perfect gas model. The effect of the gas model on temperature and specific heat ratio distributions, as well as the heat transfer and pressure coefficients over the wedge surface are investigated. The shock polar method is applied for comparison with computational results, while a 1D flow model is proposed to explain the occurrence of the quasi-normal shock wave. Finally, the effects of variations in Mach number and enthalpy are determined, by alternatively varying the two parameters around Ma=7 and h0=2.1MJ/kg at Re=4e4/m.

physics.flu-dyn↗

arXiv2024

Fourier Coefficients and Algebraic Cusp Forms on $\mathrm{U}(2,n)$

We establish a theory of scalar Fourier coefficients for a class of non-holomorphic, automorphic forms on the quaternionic real Lie group $\mathrm{U}(2,n)$. By studying the theta lifts of holomorphic modular forms from $\mathrm{U}(1,1)$, we apply this theory to obtain examples of non-holomorphic cusp forms on $\mathrm{U}(2,n)$ whose Fourier coefficients are algebraic numbers.

math.NT↗

arXiv2024

Epsilon dichotomy for twisted linear models

Let $E/F$ be a quadratic extension of local nonarchimedean fields of characteristic zero and let $D$ be a quaternion algebra over $F$ containing $E$. In this paper, we study a relation between the existence of twisted linear models on $\mathrm{GL}_n(D)$ and the local root numbers.

math.NT↗

arXiv2024

Cohomology classes, periods, and special values of Rankin-Selberg $L$-functions

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 $m=n-2$.

math.NT↗

arXiv2023

Some remarks on strong multiplicity one for paramodular forms

We establish several refined strong multiplicity one results for paramodular cusp forms by using automorphic and Galois-theoretic methods. We also give an application to distinguishing eigenforms by the twisted central values of the spinor $L$-functions, which is based on a result in Radziwi{\l}{\l} and Yang 2023 (arXiv:2304.09171).

math.NT↗

arXiv2023

Product of Rankin-Selberg convolutions and a new proof of Jacquet's local converse conjecture

In this article, we construct a family of integrals which represent the product of Rankin-Selberg $L$-functions of $\mathrm{GL}_{l}\times \mathrm{GL}_m$ and of $\mathrm{GL}_{l}\times \mathrm{GL}_n $ when $m+n<l$. When $n=0$, these integrals are those defined by Jacquet--Piatetski-Shapiro--Shalika up to a shift. In this sense, these new integrals generalize Jacquet--Piatetski-Shapiro--Shalika's Rankin-Selberg convolution integrals. We study basic properties of these integrals. In particular, we define local gamma factors using this new family of integrals. As an application, we obtain a new proof of Jacquet's local converse conjecture using these new integrals.

math.RT↗

arXiv2023

Generalizations of the Erd\H{o}s-Kac Theorem and the Prime Number Theorem

In this paper, we study the linear independence between the distribution of the number of prime factors of integers and that of the largest prime factors of integers. Respectively, under a restriction on the largest prime factors of integers, we will refine the Erd\H{o}s-Kac Theorem and Loyd's recent result on Bergelson and Richter's dynamical generalizations of the Prime Number Theorem. At the end, we will show that the analogue of these results holds with respect to the Erd\H{o}s-Pomerance Theorem as well.

math.NT↗

arXiv2023

A note on a Hecke type integral for $\mathrm{Sp}(2n)\times \mathrm{GL}(1)$

Let $\pi$ be an irreducible cuspidal automorphic generic representation of $\mathrm{Sp}_{2n}(\mathbb{A})$ and let $\chi:F^\times\backslash \mathbb{A}^\times\to \mathbb{C}^\times$ be a unitary idele class character. In this note, we present a Rankin-Selberg integral of Hecke type for the twisted standard partial $L$-function $L^S(s,\pi\times\chi)$ of degree $2n+1$.

math.NT↗

arXiv2023

$L$-functions for $\mathrm{Sp}(2n)\times\mathrm{GL}(k)$ via non-unique models

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 $\mathrm{Sp}_{2n}\times\mathrm{GL}_1$.

math.NT↗

arXiv2023

On a refined local converse theorem for SO(4)

Recently, Hazeltine-Liu, and independently Haan-Kim-Kwon, proved a local converse theorem for $\mathrm{SO}_{2n}(F)$ over a $p$-adic field $F$, which says that, up to an outer automorphism of $\mathrm{SO}_{2n}(F)$, an irreducible generic representation of $\mathrm{SO}_{2n}(F)$ is uniquely determined by its twisted gamma factors by generic representations of $\mathrm{GL}_k(F)$ for $k=1,\dots,n$. It is desirable to remove the ``up to an outer automorphism" part in the above theorem using more twisted gamma factors, but this seems a hard problem. In this paper, we provide a solution to this problem for the group $\mathrm{SO}_4(F)$, namely, we show that a generic supercuspidal representation $\pi$ of $\mathrm{SO}_4(F)$ is uniquely determined by its $\mathrm{GL}_1$, $\mathrm{GL}_2$ twisted local gamma factors and a twisted exterior square local gamma factor of $\pi$.

math.RT↗