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In this paper, for $a\in \mathbb{C}$, we investigate functions $g_{a}$ and $ \psi _{a}$ associated with three term relations. $g_{a}$ is defined by means of function $\psi _{a}$. By using these functions, we obtain some functional equations related to the Eisenstein series and the Riemann zeta function. Also we find a generalized difference formula of function $g_{a}$.
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참고문헌 (12)
참고문헌 신청
M. Abramowitz / 1972 / Handbook of Mathematical Functions
T. M. Apostol / 1976 / Modular functions and Dirichlet Series in Number Theory / Springer-Verlag
T. M. Apostol / 1976 / Introduction to Analytic Number Theory / Springer-Verlag
S. Bettin / 2013 / Period functions and cotangent sums / Algebra Number Theory 7(1):215~242
R. Bruggeman / 1997 / Automorphic forms, hyperfunction cohomology, and period functions / J. Reine Angew. Math 492:1~39
T. M. Apostol / 1976 / Modular functions and Dirichlet Series in Number Theory / Springer-Verlag
T. M. Apostol / 1976 / Introduction to Analytic Number Theory / Springer-Verlag
S. Bettin / 2013 / Period functions and cotangent sums / Algebra Number Theory 7(1):215~242
R. Bruggeman / 1997 / Automorphic forms, hyperfunction cohomology, and period functions / J. Reine Angew. Math 492:1~39
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