In this talk we will discuss the p-adic zeta-function and Hecke polynomials with Newton Polygon, respectively. Motivated by finding zeros of p-adic zeta-function, we study the irregular primes and so-called Delta-conjecture. Although this conjecture remains open, we show a sufficient condition of it by using classical theorems for the Bernoulli numbers. In the second part, we consider the generic Newton polygon of Hecke polynomials and conjecture length of the zero slope and quadratic lower bounds.