Results 11 to 20 of about 1,423 (40)
Visual properties of generalized Kloosterman sums [PDF]
, 2016 For a positive integer m and a subgroup A of the unit group (Z/mZ)x, the corresponding generalized Kloosterman sum is the function K(a, b, m, A) = ΣuEA e(au+bu-1/m).
Burkhardt, Paula, \u2716 +5 more
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The balanced Voronoi formulas for GL(n)
, 2017 In this paper we show how the GL(N) Voronoi summation formula of [MiSc2] can be rewritten to incorporate hyper-Kloosterman sums of various dimensions on both sides.
Miller, Stephen D., Zhou, Fan
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Improved bounds for Fourier coefficients of Siegel modular forms
, 2016 The goal of this paper is to improve existing bounds for Fourier coefficients of higher genus Siegel modular forms of small ...
Bringmann, Kathrin
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Bounds for twisted symmetric square $L$-functions
, 2012 Let $f\in S_k(N,\psi)$ be a newform, and let $\chi$ be a primitive character of conductor $q^{\ell}$. Assume that $q$ is a prime and $\ell>1$. In this paper we describe a method to establish convexity breaking bounds of the form $$ L(\tfrac{1}{2},\Sym f ...
Munshi, Ritabrata
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Subconvex bounds on GL(3) via degeneration to frequency zero
, 2018 For a fixed cusp form $\pi$ on $\operatorname{GL}_3(\mathbb{Z})$ and a varying Dirichlet character $\chi$ of prime conductor $q$, we prove that the subconvex bound \[ L(\pi \otimes \chi, \tfrac{1}{2}) \ll q^{3/4 - \delta} \] holds for any $\delta < 1/36$.
Holowinsky, Roman, Nelson, Paul D.
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The value distribution of incomplete Gauss sums
, 2012 It is well known that the classical Gauss sum, normalized by the square-root number of terms, takes only finitely many values. If one restricts the range of summation to a subinterval, a much richer structure emerges.
Chinen +4 more
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The hyperbolic, the arithmetic and the quantum phase
, 2003 We develop a new approach of the quantum phase in an Hilbert space of finite dimension which is based on the relation between the physical concept of phase locking and mathematical concepts such as cyclotomy and the Ramanujan sums.
Planat, Michel, Rosu, Haret
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An additive problem in the Fourier coefficients of cusp forms
, 2003 We establish an estimate on sums of shifted products of Fourier coefficients coming from holomorphic or Maass cusp forms of arbitrary level and nebentypus. These sums are analogous to the binary additive divisor sum which has been studied extensively. As
Harcos, Gergely
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The prime geodesic theorem for $\mathrm{PSL}_{2}(\mathbb{Z}[i])$ and spectral exponential sums
, 2020 We shall ponder the Prime Geodesic Theorem for the Picard manifold $\mathcal{M} = \mathrm{PSL}_{2}(\mathbb{Z}[i]) \backslash \mathfrak{h}^{3}$, which asks about the asymptotic behaviour of a counting function for the closed geodesics on $\mathcal{M ...
Kaneko, Ikuya
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The Functional Equation and Beyond Endoscopy
, 2012 In his paper "Beyond Endoscopy," Langlands tries to understand functoriality via poles of L-functions. The following paper further investigates the analytic continuation of a L-function associated to a $GL_2$ automorphic form through the trace formula ...
Herman, P. Edward
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