Back to Search
Start Over
Dirichlet Series with Periodic Coefficients and their Value-Distribution Near the Critical Line
- Source :
- Collected papers. In commemoration of the 130th birth anniversary of Academician Ivan Matveevich Vinogradov, Trudy Mat. Inst. Steklova, 2021, Vol. 314, pp. 248-274
- Publication Year :
- 2020
-
Abstract
- The class of Dirichlet series associated with a periodic arithmetical function $f$ includes the Riemann zeta-function as well as Dirichlet $L$-functions to residue class characters. We study the value-distribution of these Dirichlet series $L(s;f)$, resp. their analytic continuation in the neighborhood of the critical line (which is the abscissa of symmetry of the related Riemann-type functional equation). In particular, for a fixed complex number $a\neq 0$, we prove for an even or odd periodic $f$ the number of $a$-points of the $\Delta$-factor of the functional equation, prove the existence of the mean-value of the values of $L(s;f)$ taken at these points, show that the ordinates of these $a$-points are uniformly distributed modulo one and apply this to show a discrete universality theorem.<br />Comment: Dedicated to the Memory of Ivan Matveevich Vinogradov at the Occasion of his 130th Birthday
- Subjects :
- Mathematics - Number Theory
Mathematics - Complex Variables
11M06, 30D35
Subjects
Details
- Database :
- arXiv
- Journal :
- Collected papers. In commemoration of the 130th birth anniversary of Academician Ivan Matveevich Vinogradov, Trudy Mat. Inst. Steklova, 2021, Vol. 314, pp. 248-274
- Publication Type :
- Report
- Accession number :
- edsarx.2007.14008
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.4213/tm4188