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Zapiski Nauchnykh Seminarov LOMI, 1984, Volume 134, Pages 117–137
(Mi znsl4744)
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This article is cited in 1 scientific paper (total in 1 paper)
Значения рядов Дирихле, ассоциированных с модулярными формами, в точках $s=\frac12,1$
E. P. Golubeva, O. M. Fomenko
Abstract:
Let $f(z)=\sum_{n=1}^\infty a(n)e^{2\pi inz}$ be a cusp form of even weight $k$ which is an eigenfunction of all Hecke operators, $\chi$ a real character $\mod d$, $L_f(s,\chi)=\sum_{n=1}^\infty\chi(n)a(n)n^{-s-\frac{k-1}2}$. It is known that $L_f(s,\chi)$ satisfies a functional equation of Riemann type under $s\to1-s$. The authors prove some asymptotic results on $L_f(\frac12, \chi)$, $L_f(1, \chi)$, $d\to\infty$.
Citation:
E. P. Golubeva, O. M. Fomenko, “Значения рядов Дирихле, ассоциированных с модулярными формами, в точках $s=\frac12,1$”, Automorphic functions and number theory. Part II, Zap. Nauchn. Sem. LOMI, 134, "Nauka", Leningrad. Otdel., Leningrad, 1984, 117–137
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https://www.mathnet.ru/eng/znsl4744 https://www.mathnet.ru/eng/znsl/v134/p117
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Abstract page: | 156 | Full-text PDF : | 62 |
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