Extensions of Selberg-Delange method

Multiple Zeta function;Selberg-Delange Method;Asymptotic;Riemann Zeta function

Phaovibul, Mtip Easter

关键词: Multiple Zeta function;    Selberg-Delange Method;    Asymptotic;    Riemann Zeta function;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/78348/PHAOVIBUL-DISSERTATION-2015.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

This dissertation involves two topics in analytic number theory. The first topic focuses on extensions of the Selberg-Delange Method, which are discussed in Chapters $2$ and $3$.The last topic, which is discussed in Chapter $4$, is a new identity for Multiple Zeta Values.The Selberg-Delange method is a method that is widely used to determine the asymptotic behavior of the sum of arithmetic functions whose corresponding Dirichlet's series can be written inthe term of the Riemann zeta function, $\zeta(s)$.In Chapter $2$, we first provide a history and recent developments of the Selberg-Delange method.Then, we provide a generalized version of the Selberg-Delange method which can be applied to a larger class of arithmetic functions. We devote Chapter $3$ to the proofs of the results stated in Chapter $2$.In $1961$, Matsuoka evaluated $\zeta(2)$by means of evaluating the integral $\ds \int_0^{\pi/2} x^{2}\cos^{2n}(x) dx$. The last chapter of this dissertation generalizes the idea of Matsuoka and obtains a new identity for Multiple Zeta Values.