Twisted Hilbert modular L-functions and spectral theory

2014/02/06 by Gergely Harcos, Harcos, Gergely
Mathematics · #11E20 #11E45 #11F70 #11F72 #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Primary 11F41 #Secondary 11E12

paper · pdf · doi:10.48550/arxiv.1402.1332

openalex publication_date 2014/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

These are notes for four lectures given at the 2010 CIMPA Research School "Automorphic Forms and L-functions" in Weihai, China. The lectures focused on a Burgess-like subconvex bound for twisted Hilbert modular L-functions published jointly with Valentin Blomer in the same year. They discussed the proof in some detail, especially how spectral theory can be used to estimate the relevant shifted convolution sums efficiently. They also discussed briefly an application for the number of representations by a totally positive ternary quadratic form over a totally real number field.

Citations

• Shifted convolution sums and Burgess type subconvexity over number fields
• On Modular Forms of Half Integral Weight

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