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An inequality for the Riemann zeta function
We consider an inequality concerning absolute values of the Riemann zeta function at places symmetric with respect to the critical line. The study...
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The Generalized Riemann Hypothesis from zeros of the zeta function
We show that the Generalized Riemann Hypothesis for Dirichlet L -functions is a consequence of certain conjectural properties of the zeros of the...
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The Riemann zeta function on arithmetic progressions and denseness properties
In recent joint work with Sourmelidis, Steuding and Suriajaya, the author studied the distribution of values of the Riemann zeta function on...
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Riemann–Hurwitz theorem and Riemann–Roch theorem for hypermaps
In this paper, we try to answer some questions raised by Cangelmi (Eur J Comb 33(7):1444–1448, 2012). We reinterpret the Riemann–Hurwitz theorem of...
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The Riemann Zeta Function
The Dirichlet series \(D(\mathbbm {1},s)\)...
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a-Points of Partial Sums of the Riemann Zeta Function
We study the a-points of partial sums of the Riemann zeta function for any a ∈ ℂ. Our main goal is to understand where in the complex plane do the...
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Five Hilbert Space Models Related to the Riemann Zeta Function
In a recent work of the author, a de Branges space was constructed, as well as an operator on it whose spectrum coincides with the set of nontrivial...
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Schoenberg’s Theory of Totally Positive Functions and the Riemann Zeta Function
This chapter is a short survey of some aspects and applications of Schoenberg’s work on totally positive functions. Totally positive functions arise...
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Calculation of the Values of the Riemann Zeta Function Via Values of its Derivatives at a Single Point
We consider the following two problems. We are given the values of several initial derivatives of the Riemann zeta function calculated at some...
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The Riemann Hypothesis for Function Fields
In this chapter k is a finite field of characteristic p with q elements. Let F be an algebraic function field of one variable over K and g the genus...
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The prime number theorem and pair correlation of zeros of the Riemann zeta-function
We prove that the error in the prime number theorem can be quantitatively improved beyond the Riemann Hypothesis bound by using versions of...
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The Riemann problem with delta initial data with Dirac delta function in both components for a pressureless gas dynamic model
In this paper, we study the Riemann problem with the initial data containing the Dirac delta function in both components for a nonstrictly hyperbolic...
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Universality Theorem for the Iterated Integrals of the Logarithm of the Riemann Zeta-Function
In this paper, we prove the universality theorem for the iterated integrals of the logarithm of the Riemann zeta-function on a line parallel to the...