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In this paper, we study the value distribution of the derivative of a Dirichlet $L$-function $L'(s,\chi)$ at the $a$-points $\rho_{a,\chi}=\beta_{a,\chi}+i\gamma_{a,\chi}$ of $L(s,\chi).$ We give an asymptotic formula for the sum $$\sum_{\rho_{a,\chi};\ 0<\gamma_{a,\chi}\leq T}L'\left(\rho_{a,\chi},\chi\right) X^{\rho_{a,\chi}}\ \ \hbox{as}\ \ T\rightarrow \infty,$$ where $X$ is a fixed positive number and $\chi$ is a primitive character $\!\!\mod q$. This work continues the investigations of Fujii \cite{2,3,4}, Garunk$\rm\check{s}$tis \& Steuding \cite{7} and the authors \cite{12}.
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참고문헌 (20)
참고문헌 신청
H. Davenport / 1980 / Multiplicative Number Theory / Springer
A. Fujii / 1987 / Uniform distribution of the zeros of the Riemann zeta function and the mean value theorems of Dirichlet L-functions / Proc. Japan Acad. Ser. A Math. Sci 63(9):370~373
A. Fujii / 1988 / Zeta zeros and Dirichlet L-functions / Proc. Japan Acad. Ser. A Math. Sci 64(6):215~218
A. Fujii / 1991 / Some observations concerning the distribution of the zeros of the Zeta func-tions. II / Comment. Math. Univ. St. Pauli 40(2):125~231
A. Fujii / 1994 / On a conjecture of Shanks / Proc. Japan Acad. Ser. A Math. Sci 70(4):109~114
A. Fujii / 1987 / Uniform distribution of the zeros of the Riemann zeta function and the mean value theorems of Dirichlet L-functions / Proc. Japan Acad. Ser. A Math. Sci 63(9):370~373
A. Fujii / 1988 / Zeta zeros and Dirichlet L-functions / Proc. Japan Acad. Ser. A Math. Sci 64(6):215~218
A. Fujii / 1991 / Some observations concerning the distribution of the zeros of the Zeta func-tions. II / Comment. Math. Univ. St. Pauli 40(2):125~231
A. Fujii / 1994 / On a conjecture of Shanks / Proc. Japan Acad. Ser. A Math. Sci 70(4):109~114
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