The evaluations of determinants with Legendre symbol entries have close relation combinatorics and character sums over finite fields. Recently, Sun [9] posed some conjectures on this topic. In paper, we prove also study variants. For example, show the following result:

identity is one of those symbols which are influenced by variety of factors. since civilization and culture consists of physical and spiritual manifestations left behind by the mankind throughout the history, the tools and the items used by them becomes extremely important when studying their culture. by studying the symbols and the myths which are reflection of the people who used these items,...

in this paper we study properties of symbols such that these belong to class of symbols sitting insidesm ρ,φ that we shall introduce as the following. so for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of m−hypoelliptic pseudodifferential operators for which define base on this class of symbols. also we consider maxi...