TY - JOUR TI - The method for the heat-diffusion equation in analytic number theory AU - Yang Xiao-Jun AU - Alshehri Ahmed AU - Cui Ping JN - Thermal Science PY - 2023 VL - 27 IS - 5 SP - 3837 EP - 3844 PT - Article AB - This paper addresses the entire functions via theory of the tempered xi function. The zeros of the entire functions by the Fourier sine and cosine integrals are studĀ­ied in detail. The method for the heat-diffusion equation is proposed to structure the connection between Fourier analysis and heat-diffusion equation show the open problems in analytic number theory.