Sup-norm bounds for Eisenstein series
-
Bingrong Huang
and
Zhao Xu
Abstract
The paper deals with establishing bounds for Eisenstein series on congruence quotients of the upper half plane, with control of both the spectral parameter and the level. The key observation in this work is that we exploit better the structure of the amplifier by just supporting on primes for the Eisenstein series, which can use both the analytic method as Young did to get a lower bound for the amplifier and the geometric method as Harcos–Templier did to obtain a more efficient treatment for the counting problem.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11531008
Award Identifier / Grant number: 11501327
Funding statement: The first author is supported in part by the project of the National Natural Science Foundation of China (11531008), and the second author is supported by the project of the National Natural Science Foundation of China (11501327).
Acknowledgements
The authors would like to thank Professor Jianya Liu for his constant encouragement. They would also like to thank the referee for very useful suggestions and comments, which make our Theorem 2 much better than the original version.
References
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Articles in the same Issue
- Frontmatter
- The role of the Rogers–Shephard inequality in the characterization of the difference body
- Test vectors for local periods
- The local Langlands conjecture for p-adic GSpin4, GSpin6, and their inner forms
- A family of irretractable square-free solutions of the Yang–Baxter equation
- On Sylow permutable subgroups of finite groups
- Using Steinberg algebras to study decomposability of Leavitt path algebras
- The ℓ∞-semi-norm on uniformly finite homology
- Minimal potential results for Schrödinger equations with Neumann boundary conditions
- On a unique continuation for Aharonov–Bohm magnetic Schrödinger equation
- Sup-norm bounds for Eisenstein series
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Permutohedral structures on
- On the complete integrability of the periodic quantum Toda lattice
-
Fans, decision problems and generators of free abelian
- Standard cocycles: Variations on themes of C. Kassel’s and R. Wilson’s
- Crossed modules as maps between connected components of topological groups
- A local converse theorem for U(2,2)
- Probabilistic trace and Poisson summation formulae on locally compact abelian groups
