Results 41 to 50 of about 137,956 (119)
ON THE FOURTH POWER MEAN OF GENERALIZED TWO-TERM EXPONENTIAL SUMS [PDF]
Bulletin of the Korean Mathematical Society, 2013 In this paper, we use the elementary method and the theory of complex functions to study the computational problem of the fourth power mean of the generalized two-term exponential sums, and give two exact identities for them.
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Exponential Sums Related to Maass Forms [PDF]
, 2015 We estimate short exponential sums weighted by the Fourier coefficients of a Maass form. This requires working out a certain transformation formula for non-linear exponential sums, which is of independent interest.
Jääsaari, Jesse, Vesalainen, Esa V.
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Computing Dirichlet character sums to a power-full modulus
, 2014 The Postnikov character formula is used to express large portions of a Dirichlet character sum in terms of quadratic exponential sums. The quadratic sums are then computed using an analytic algorithm previously derived by the author.
Hiary, Ghaith A.
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Short-Interval Averages of Sums of Fourier Coefficients of Cusp Forms
, 2016 Let $f$ be a weight $k$ holomorphic cusp form of level one, and let $S_f(n)$ denote the sum of the first $n$ Fourier coefficients of $f$. In analogy with Dirichlet's divisor problem, it is conjectured that $S_f(X) \ll X^{\frac{k-1}{2} + \frac{1}{4 ...
Hulse, Thomas A. +3 more
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Aspects of Relativistic Sum Rules
, 2004 The status of our understanding of relativistic sum rules is reviewed. The recent development of new theoretical methods for the evaluation of these sum rules offers hope for further advances in this challenging field. These new techniques are described,
Aucar +43 more
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Level Spacings for Integrable Quantum Maps in Genus Zero
, 2000 We consider the eigenvalue pair correlation problem for certain integrable quantum maps on the 2-sphere. The classical maps are time one maps of Hamiltonian flows of perfect Morse functions.
Zelditch, Steve
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Scattering a pulse from a chaotic cavity: Transitioning from algebraic to exponential decay
, 2008 The ensemble averaged power scattered in and out of lossless chaotic cavities decays as a power law in time for large times. In the case of a pulse with a finite duration, the power scattered from a single realization of a cavity closely tracks the power
C. E. Porter +5 more
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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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On the generalized exponential sums and their fourth power mean
Open MathematicsThe main purpose of this article is to study the calculating problem of the fourth power mean of the two-term exponential sums and provide an accurate calculating formula for utilizing analytical methods and character sums’ properties. In the meantime, a
Liu Wencong, Ning Shushu
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The hybrid power mean of the generalized Gauss sums and the generalized two-term exponential sums
AIMS Mathematics<abstract><p>This article applied the properties of character sums, quadratic character, and classical Gauss sums to study the calculations of the hybrid power mean of the generalized Gauss sums and the generalized two-term exponential sums. It also provided exact formulas for calculating these hybrid power means.</p></abstract>
Xue Han, Tingting Wang
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