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Showing 1 to 7 of 7 for “"Dirichlet Characters"”.
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Vanishing and non-vanishing of L-series of elliptic curves twisted by Dirichlet characters
… of L -series of elliptic curves twisted by Dirichlet characters. In particular, we study the vanishing and non vanishing of these L -series at the critical point. We present empirical results indicating the vanishing behaviour of cyclic twists of orders 3, 5, 7 and conductors up to 5000 for …
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A Detailed Proof of the Prime Number Theorem for Arithmetic Progressions
… progressions. We will review basic results from Dirichlet characters and L-functions. Furthermore, we establish a weak version of the Wiener-Ikehara Tauberian Theorem, which is an essential tool for the proof of our main result.
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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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Moments Of Products Of L-Functions
… of automorphic L-functions twisted by quadratic Dirichlet characters and averaged over fundamental discriminants. These results were proved jointly with Micah B. Milinovich.
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L-functions and J-spectra
… the Riemann ζ-functions and Eisenstein series by Dirichlet characters. We first explain congruences of these twisted Eisenstein series of level Γ_1(N) and character χ via the Dieudonné theory of height 1 formal groups and formal A-modules and their finite subgroups. Our approach is based on Katz’s …
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Topics in Multiplicative and Probabilistic Number Theory
… size of partial sums of odd order non-principal Dirichlet characters, both unconditionally and assuming the Generalized Riemann Hypothesis, and show that our conditional results are nearly best possible unconditionally. We also prove a quantitative bivariate Erdo&huml;s-Kac theorem on the joint …
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Transformation formulas associated with integrals involving the Riemann Ξ-function and rank-crank type PDEs in partition theory
… the results from Chapters 3 and 4 for primitive Dirichlet characters. These are of the form $F(z, \alpha,\chi)=F(-z, \beta,\overline{\chi})=F(-z,\alpha,\overline{\chi})=F(z,\beta,\chi)$, where $\alpha\beta=1$. Character analogues of the Hurwitz zeta function and digamma function make their …