Eisenstein series and their applications to some arithmetic identities and congruences

Abstract

Utilizing the theory of elliptic curves over ℂ to the normalized lattice Aτ, its connection to the Weierstrass p-functions and to the Eisenstein series E4(τ) and E6(τ), we establish some arithmetic identities involving certain arithmetic functions and convolution sums of restricted divisor functions. We also prove some congruence relations involving certain divisor functions and restricted divisor functions. © 2013 Kim et al.