Differential polynomials of L-functions with truncated shared values

Uniqueness of meromorphic functions ans Q-differential polynomials sharing small functions

‎The paper concerns interesting problems related to the field of Complex Analysis‎, ‎in particular, Nevanlinna theory of meromorphic‎ ‎functions‎. ‎We have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a‎ ‎small function‎. ‎Outside‎, ‎in this paper‎, ‎we also consider the uniqueness of $q-$ shift difference‎ - ‎differential polynomials‎ ‎of mero...

Fractional differential equations with Legendre polynomials

Twisted Hecke L-values and Period Polynomials

Let f1, . . . , fd be an orthogonal basis for the space of cusp forms of even weight 2k on Γ0(N). Let L(fi, s) and L(fi, χ, s) denote the L-function of fi and its twist by a Dirichlet character χ, respectively. In this note, we obtain a “trace formula” for the values L(fi, χ,m)L(fi, n) at integers m and n with 0 < m, n < 2k and proper parity. In the case N = 1 or N = 2, the formula gives us a c...

Uniqueness of Meromorphic Functions of Differential Polynomials Sharing Two Values IM

In this paper, we shall study the uniqueness problems of meromorphic functions of differential polynomials sharing two values IM. Our results improve or generalize many previous results on value sharing of meromorphic functions.

Period polynomials, derivatives of L-functions, and zeros of polynomials

Period polynomials have long been fruitful tools for the study of values of L-functions in the context of major outstanding conjectures. In this paper, we survey some facets of this study from the perspective of Eichler cohomology. We discuss ways to incorporate non-cuspidal modular forms and values of derivatives of L-functions into the same framework. We further review investigations of the l...