Examples of Bessel Functions of Order Zero Related to the Functional Equation of the Riemann Zeta Function
Hideto Iwata
Abstract
In 2010, M. A. Chaudhry et al. introduced a class of functions Sigma satisfying an L1-condition. They proved that every function phi in Sigma gives rise to the functional equation for the Riemann zeta function. They also provided an example of a function outside Sigma for which the functional equation still holds. In this paper, we present several examples of Bessel functions of order zero that do not belong to Sigma but nevertheless give rise to the functional equation for the Riemann zeta function. In particular, we show that J0(a sqrt(x)), J0(ax), and Y0(x) exhibit this phenomenon.
Create a lesson
Related papers
Kitaoka's conjecture for real cyclotomic fields
Jakub Krásenský
Proof of Two Conjectural q-Supercongruences Related to Van Hamme's (G.2) Supercongruence
Liton Karmakar, Arijit Jana
Exact Rank of the Largest Good Lattice Point Matrix
Long-Hao Xu
Bounds for (k,c) model functions over p-adic fields
Eyal Kaplan
On trace-zero norm forms of orders of rational quaternion algebras with applications
Yifan Luo, Tianze Wang, Haigang Zhou
Simultaneous Unimodularity of Positive Integer Matrices and Their Entrywise Cubes
Xinyi Li, Shuochen Wang, Zimeng Ye et al.