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Showing 1 to 15 of 15 for “"Dirichlet series"”.
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On the Summatory Functions of a Class of Dirichlet Series
Made available in DSpace on 2014-12-14T13:09:33Z (GMT). No. of bitstreams: 1 7709153.pdf: 3320802 bytes, checksum: 850b85e19c4d4c1dcd96f4919a30e96a (MD5) Previous issue date: 1976
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Hecke Correspondence for Automorphic Integrals with Infinite Log-Polynomial Periods
… Hecke first proved his correspondence between Dirichlet series with functional equations and automorphic forms, there have been a great number of generalizations. Of particular interest is a generalization due to Bochner that gives a correspondence between Dirichlet series with any finite …
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On the Average Order of the Divisor Function, Lattice Point Functions, and Other Arithmetical Functions
… class of arithmetical functions generated by Dirichlet series satisfying a very general functional equation with gamma factors. We obtain one and two-sided (OMEGA)-theorems for the error terms associated with certain weighted averages of these arithmetical functions. For example, if {a(n)} is …
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Whittaker functions on metaplectic groups
… of reductive groups in the theory of multiple Dirichlet series, we provide a study of Whittaker functions on metaplectic covers of reductive groups over local fields.
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Distribution of sequences related to L-functions
… part of this thesis, we expand the class of Dirichlet series whose monotonicity properties are known. In particular, we describe a large class of Dirichlet series that are not logarithmically completely monotonic. Using similar techniques, an equivalent formulation of the Riemann Hypothesis …
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Combinatorial aspects of root lattices and words
… by means of a particular quaternion algebra. Dirichlet series generating functions are derived, which count the number of similar sublattices, respectively coincidence site lattices, of each index. In the second part, several strategies to derive upper and lower bounds for the entropy of …
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Adelic Fourier-Whittaker coefficients and the Casselman-Shalika formula
… these representations fall into a principle series, indexed by characters on a torus of the metaplectic group, and there is an associated an L-function. In the final section of their paper, an equivalence is shown in the rank one case between this -function and an Dirichlet series defined …
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Secondary Terms in Asymptotics for the Number of Zeros of Quadratic Forms
… work classically to exploit Gauss sums and find Dirichlet characters that fit into the odd degree case. We also provide an explicit description of the Dirichlet series arisen during the investigation, which is useful in applications. It turns out that the geometric interpretation of the constant …
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Visibility of lattice points in high dimensional spaces and extreme values of combinations of Dirichlet L-functions
… thesis, we work with large values of certain Dirichlet series and their partial sums. In particular, we examine a `short' partial sum of the Riemann Zeta function, $\zeta_N(s) = \sum_{n\le N}\frac{1}{n^s}$. We obtain large values of $\zeta_N\left(\frac{1}{2}+it\right)$ for $t\in[\sqrt{T}, T]$ …
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Local behavior of distributions and applications
… tauberian theory, summability of divergent series and integrals, and number theory. In Chapter 2 we give two new proofs of the Prime Number Theory based on ideas from asymptotic analysis on spaces of distributions. Several inverse problems in Fourier analysis and summability theory are …
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Asymptotic formulae for certain arithmetic functions produced by fractional linear transformations
K.T. Atanassov introduced the two arithmetic functions \[ I(n) = \prod_{\nu=1}^k p_\nu^{1/\alpha_\nu} \qquad \text{and}\qquad R(n) = \prod_{\nu=1}^k p_\nu^{\alpha_v - 1} \] called the irrational factor and the strong restrictive factor, respectively. A variety of authors have studied the properties …
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Topics in number theory
… associated with the coefficients of the Dirichlet series representations for [formula] On the same topic results are proven about connections between RH (σ₀) and the distribution of the set HN of Farey numbers of order N. Some general theorems concerning the sums [formula] are established …
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Counterexamples related to the Sato-Tate conjecture
Let $E_{/\mathbf{Q}}$ be an elliptic curve. The Sato--Tate conjecture, now a theorem, tells us that the angles $\theta_p =\cos^{-1}\left(\frac{a_p}{2\sqrt p}\right)$ are equidistributed in $[0,\pi]$ with respect to the measure $\frac{2}{\pi}\sin^2\theta\, d\theta$ if $E$ is non-CM …
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Topics on the Spectral Theory of Automorphic Forms
… study the analytic properties of the Eisenstein Series of $frac {1}{2}$-integral weight associated with the Hecke congruence subgroup $Gamma_0(4)$. Using these properties we obtain asymptotics for sums of certain Dirichlet $L$-series. We also obtain a formula reducing the study of Selberg's …