On triple product L-functions and the fiber bundle method

2025/03/27 by Getz, Jayce R., Gu, Miao Pam, Hsu, Chun-Hsien +1 · 2 citations
#11F66 #11F70 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2503.21648

Abstract

We introduce multi-variable zeta integrals which unfold to Euler products representing the triple product L-function times a product of L-functions with known analytic properties. We then formulate a generalization of the Poisson summation conjecture and show how it implies the analytic properties of triple product L-functions. Finally, we propose a strategy, the fiber bundle method, to reduce this generalized conjecture to a simpler case of the Poisson summation conjecture along with certain local compatibility statements.

Cited by

• Modulation groups
• Triple product L-functions and the Ramanujan conjecture

Related

• Analysis of Zeta Functions, Multiple Zeta Values, and Related Integrals
• Riemann's Zeta Function and Beyond
• Explicit formulas of the relation between multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types
• Triple product L-functions and the Ramanujan conjecture
• Algebraicity of critical values of triple product L-functions in the balanced case