Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms
By Charles Li, Andrew H. Knightly. 2012
70 citations recorded by the source corpus.
Introduction Preliminaries Bi-$K_\infty$-invariant functions on $\operatorname{GL}_2(\mathbf{R})$ Maass cusp forms Eisenstein series The kernel of $R(f)$ A Fourier trace formula for $\operatorname{GL}(2)$ Validity of the KTF for a broader class of $h$ Kloosterman sums Equidistribution of Hecke eigenvalues Bibliography Notation index Subject index
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e3c58b8a4b34838d203a063de33352426723a9d4
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In Algebra and Number Theory
In Mathematical Physics
Citations in the corpus
- Sums of Kloosterman sums in arithmetic progressions, and the error term in the dispersion method (2015, unknown): “When c is prime, the Weil bound ( cf. [ KL13 , Theorem 9.3]) from algebraic geometry can be used.”
- Explicit calculations with Eisenstein series (2017, background): “sps, then (3.2) Eγa(z,s,ψ) = ψ(γ)E a(z,s,ψ), correcting a remark of [DFI, p.505]. 3.2. Eisenstein series attached to characters. We draw inspiration from Huxley’s paper [Hux], but refer the reader to [KL] for a more motivated definition. Let χ1,χ2 be Dirichlet characters modulo q1,q2, respectively, w”
- Twisted moments of L-functions and spectral reciprocity (2017, methodology): “GJ], and the Fourier expansion of these Eisenstein series is computed explicitly in [KL, Section 5] (see [BH, Section 2.7] for similar calculations over number fields). In the following, we quote from [KL]. In the notation of [KL] we have M= Q pip. We define as in [KL, (5.22)] (3.3) n2(M) := 1 M Y p|N”