Open AccessThe Proof for A Convergent Integral and Another Nonzero Integral--Respectively Using the Riemann Zeta Function and the Trigonometric Sums
Author(s) -
Hao-Cong Wu
Publication year - 2016
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v8n4p74
Subject(s) - mathematics , riemann zeta function , arithmetic zeta function , exponential integral , laplace transform , riemann hypothesis , mathematical proof , trigonometry , pure mathematics , prime zeta function , mathematical analysis , improper integral , integral equation , volume integral , fourier integral operator , geometry
In this paper, there are the applications of the main inequalities, and show how to use the analytic properties of the Zeta function and the Laplace transform to prove the convergence of the desired integral. In addition, show how to use the trigonometric sums and the mathematical induction with the method of infinite descent to prove the non-zero value of another integral. In this way, we can obtain the important proofs concerning the Riemann Zeta function and the sum of two primes.