| Title |
Discrete moments of the Riemann zeta function and Dirichlet L-functions / |
| Translation of Title |
Riemann'o dzeta funkcijos ir Dirichlet L-funkcijų diskretieji momentai. |
| Authors |
Kalpokas, Justas |
| Full Text |
|
| Pages |
84 |
| Keywords [eng] |
Riemann zeta ; Dirichlet ; critical line |
| Abstract [eng] |
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems that concern the integers. It is often said to have begun with Dirichlet's introduction of Dirichlet L-functions. In analytic number theory one of the main investigation objects is the Riemann zeta function. The Riemann hypothesis states that all non-trivial zeros of the Riemann zeta function lie on the critical line. In the thesis we investigate value distribution of the Riemann zeta function on the critical line. To do so we use the curve of the Riemann zeta function on the critical line. A problem connected to the curve asks the question whether the curve is dense in the complex plane. We prove that the curve expands to all directions on the complex plane. A separete case of the main result can be stated as follows Riemann zeta function has infinetly many negative values on the critical line and they are unbounded. |
| Type |
Doctoral thesis |
| Language |
English |
| Publication date |
2012 |
