Add to ORKGWe study Riemann-type functional equations with respect to value-distribution theory and derive implications for their solutions. In particular, for a fixed complex number $a\neq0$ and a function from the Selberg class $\mathcal{L}$, we prove a Riemann-von Mangoldt formula for the number of a-points of the $\Delta$-factor of the functional equation of $\mathcal{L}$ and an analog of Landau's formula over these points. From the last formula we derive that the ordinates of these $a$-points are uniformly distributed modulo one. Lastly, we show the existence of the mean-value of the values of $\mathcal{L}(s)$ taken at these points.Comment: 28 pages, a part of the original version uploaded last yea
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We offer a solution to a functional equation using properties of the Mellin transform. A new criteri...
AbstractThis is the second in a series of three papers; the other two are “Summation Formulas, from ...
We present many novel results in number theory, including a double series formula for the natural lo...
We prove explicit formulae for $\alpha$-points of $L$-functions from the Selberg class. Next we exte...
We prove an equivalent of the Riemann hypothesis in terms of the functional equation (in its asymmet...
We prove that every functional equation of Riemann's type has infinitely many linearly independent s...
The class of Dirichlet series associated with a periodic arithmetical function $f$ includes the Riem...
We formulate a generalization of Riesz-type criteria in the setting of $L$-functions belonging to th...
In this work we consider Dirichlet polynomials that belong to the extended Selberg class. Functions ...
We are concerned with an estimate and a mean square theorem for the summatory function of a class of...
Abstract: An equivalent, but variant form of Riemann's functional equation is explored, and sev...
The Riemann zeta function has a deep connection to the distribution of primes. In 1911 Landau proved...
Abstract Speiser showed that the Riemann hypothesis is equivalent to the absence of non-trivial zero...
Abstract: In this article we establish the zero-free region of certain Dirichlet polynomials LF;X ar...
AbstractThe function S(T) is the error term in the formula for the number of zeros of the Riemann ze...
We offer a solution to a functional equation using properties of the Mellin transform. A new criteri...
AbstractThis is the second in a series of three papers; the other two are “Summation Formulas, from ...
We present many novel results in number theory, including a double series formula for the natural lo...