Pan Yan

Interests

Research

Number Theory and Representation Theory.

Courses

Scholarly Contributions

Journals/Publications

• Jin, Y., & Yan, P. (2025). L-functions for Sp(2n)xGL(k) via non-unique models. International Mathematics Research Notices, 2025. doi:https://doi.org/10.1093/imrn/rnaf035
• Xue, H., & Yan, P. (2025). Epsilon dichotomy for twisted linear models. Pacific J. Math., 334(1), 59--106. doi:https://doi.org/10.2140/pjm.2025.334.59
• Yan, P. (2024). A note on a Hecke type integral for Sp(2n) × GL(1). Journal of the Ramanujan Mathematical Society, 39, 13-20.
• Yan, P., & Zhang, Q. (2024). ON A REFINED LOCAL CONVERSE THEOREM FOR SO(4). Proceedings of the American Mathematical Society, 152(11). doi:10.1090/proc/16945
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  Recently, Hazeltine-Liu, and independently Haan-Kim-Kwon, proved a local converse theorem for SO2n(F) over a p-adic field F, which says that, up to an outer automorphism of SO2n(F), an irreducible generic representation of SO2n(F) is uniquely determined by its twisted gamma factors by generic representations of GLk(F) for k = 1, . . ., 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 SO4(F), namely, we show that a generic supercuspidal representation π of SO4(F) is uniquely determined by its GL1, GL2 twisted local gamma factors and a twisted exterior square local gamma factor of π.
• Yan, P., & Zhang, Q. (2024). On a refined local converse theorem for SO(4). Proc. Amer. Math. Soc., 152(11), 4959--4976. doi:https://doi.org/10.1090/proc/16945
• Wang, B., Wei, Z., Yan, P., & Yi, S. (2023). Generalizations of the Erdős–Kac Theorem and the Prime Number Theorem. Communications in Mathematics and Statistics. doi:10.1007/s40304-023-00354-6
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  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. Under a restriction on the largest prime factors of integers, we will refine the Erdős–Kac Theorem and Loyd’s recent result on Bergelson and Richter’s dynamical generalizations of the Prime Number Theorem, respectively. At the end, we will show that the analogue of these results holds with respect to the Erdős–Pomerance Theorem as well.
• Yan, P. (2023). THE UNRAMIFIED COMPUTATION OF A SHIMURA INTEGRAL FOR SL(2) × GL(2). Rocky Mountain Journal of Mathematics, 53(4). doi:10.1216/rmj.2023.53.1313
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  We revisit the Rankin–Selberg integral of Shimura type for generic representations of SL2 × GL2 constructed by Ginzburg, Rallis, and Soudry. We give a different and more “intrinsic” proof of the unramified computation. In contrast to their proof we avoid the local functional equation for the general linear groups but use the Casselman–Shalika formulas for unramified Whittaker functions for SL2 and GL2