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Dirichlet Characters
In this chapter we introduce the preliminary tools. These include Dirichlet characters, Gauss sums, Dirichlet L-functions and Bernoulli numbers.
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Asymptotics of Generalized Partial Theta Functions with a Dirichlet Character
We prove asymptotic expansions of generalized partial theta functions with a nonprincipal Dirichlet character and relate these expansions to certain L -series....
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Three conjectures about character sums
We establish that three well-known and rather different looking conjectures about Dirichlet characters and their (weighted) sums, (concerning the...
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Character Gamma Functions and Evaluation of Series with Dirichlet L-Value Coefficients
In this paper, we demonstrate a character analogue of the Lerch formula and multiplication formulas for the Dirichlet L -functions. These formulas...
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Arithmetic progressions of squares and multiple Dirichlet series
We study a Dirichlet series in two variables which counts primitive three-term arithmetic progressions of squares. We show that this multiple...
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A note on exceptional characters and non-vanishing of Dirichlet L-functions
We study non-vanishing of Dirichlet L -functions at the central point under the unlikely assumption that there exists an exceptional Dirichlet...
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The first moment of quadratic Dirichlet L-functions at central values
We obtain an asymptotic formula for the smoothly weighted first moment of quadratic Dirichlet L -functions at central values, with explicit main terms...
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Domination of nonlinear semigroups generated by regular, local Dirichlet forms
In this article we study perturbations of local, nonlinear Dirichlet forms on arbitrary topological measure spaces. As a main result, we show that...
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Proportion of distinct zeros of a Dirichlet L-series
By studying the distribution of zeros of combinations of a Dirichlet L -function and its first-order derivative, we prove that every Dirichlet L -functi...
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Compact linear combinations of composition operators on Hilbert spaces of Dirichlet series
We study linear combinations of two composition operators induced by linear symbols on the Hilbert space of Dirichlet series. Based on partial...
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Analytical Dirichlet Series
We use the Dirichlet series of a complex argument. When n is a positive integer and...
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Multiple Lucas–Dirichlet Series Associated With Additive and Dirichlet Characters
In this article, we obtain the analytic continuation of the multiple shifted Lucas zeta function, multiple Lucas L -function associated with Dirichlet...
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The Dirichlet Space
The notes below are a copy of a set of three lectures presented online in July 2021, during the Fields Institute Focus Program Analytic Function...
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The Vladimirov–Taibleson operator: inequalities, Dirichlet problem, boundary Hölder regularity
We study the Vladimirov–Taibleson operator, a model example of a pseudo-differential operator acting on real- or complex-valued functions defined on...
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Bounds for moments of Dirichlet L-functions to a fixed modulus
We study the 2 k -th moment of central values of the family of Dirichlet L -functions to a fixed prime modulus. We establish sharp lower bounds for all...