Han WU 吴涵

Research Interests:

Analytic Number Theory, Automorphic Representation Theory

Publications:

-- Analytic Number Theory:

[12] (joint with Z.Luo and Q.Pi) Bias of root numbers for Hilbert newforms of cubic level. JNT 243 (2023), pp 62-116 (Arxiv | Journal )

[13] (joint with N.Andersen) Hybrid subconvexity and the partition function. JNT 242 (2023), pp 154-180 (ArXiv | Journal )

[7] Explicit subconvexity for $GL_2$. Mathematika 68(3) (2022), pp 921-978 ( Arxiv | Journal )

[9] (joint with G.Cherubini & G.Zabradi) On Kuznetsov-Bykovskii's formula of counting prime geodesics. Math.Z. 300 (2021), pp 881-928 ( Arxiv | Journal )

[4] Explicit Burgess-like subconvex bounds for $GL_2 \times GL_1$. Forum Math.32(5) (2020), pp 1211-1251. ( Arxiv | Journal )

[3] Burgess-like subconvexity for $GL_1$. Compo.Math.115 (2019), pp 1457-1499. ( Arxiv | Journal )

[1] Burgess-like subconvex bounds for $GL_2 \times GL_1$. Geom.Func.Analysis.24(3) (2014), pp 968-1036. ( Arxiv | Journal )

-- Analytic Theory of Automorphic Representation:

[10] On Motohashi's formula: Trans.AMS.375(11) (2022), pp 8033-8081 (Arxiv | Journal )

[8] Deducing Selberg trace formula via Rankin-Selberg method for $GL_2$. Trans.AMS.372(12) (2019), pp 8507-8551 ( Arxiv | Journal )

[5] A note on spectral analysis in automorphic representation theory for $GL_2$: I. IJNT.13(10) (2017), pp 2717-2750 ( Arxiv | Journal )

Pre-Publications:

[15] On a generalization of Motohashi's formula. (Arxiv)

[14] (joint with P.Xi) A uniform Weyl bound for $L$-functions of Hilbert modular forms. (Arxiv)

[11] (joint with O.Balkanova & D.Frolenkov) On Weyl's subconvex bound for cube-free Hecke characters: totally real case. (Arxiv)(Video 1, Video 2, Video 3 by D.Frolenkov, Video 4; Slides)

In Preparation:

[6] A note on spectral analysis in automorphic representation theory for $GL_2$: II.

[2] Subconvex bounds for compact toric integrals. under revision (Arxiv)

(Mini-)Courses:

• An Introduction to the Analytic and Spectral Theory of Automorphic Representations (Course given at YMSC Tsinghua, Sep.2016-Dec.2016). Course Notes: Spectral Analysis for $GL_2$

• Introduction to Algebraic Exponential Sums, an Artin-Schreier Case (Minicourse given at Xi'an Jiaotong University, 04 & 06 December 2018). Course Notes: Algebraic Exponential Sums

• Michel-Venkatesh Method on Subconvexity (Lecture series given at QMUL, Mar.2020-Apr.2020). Lecture Notes: Michel-Venkatesh Method

• Basic Introduction to Integral Representations of L-Functions (Lecture series given at Shandong University, 14-18 Aug. 2023). Lecture Notes: Basic Introduction to Integral Representations of L-Functions 

• Topics in Number Theory (Graduate Course at USTC, Spring 2024). Lecture Notes: Introduction to Automorphic Representations

Curriculum Vitae:

• • English version