Abstract
In a fundamental paper [S], Selberg defined a general class of Dirichlet series and formulated basic conjectures concerning them. Selberg’s conjectures concern Dirichlet series, which admit analytic continuations, Euler products and functional equations.
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References
E. Artin, Collected papers, Springer-Verlag, New York-Berlin, 1982.
S. Bochner, On Riemann’s functional equation with multiple gamma factors, Annals of Mathematics, 67 (1958) 29–41.
B. Conrey and A. Ghosh, On the Selberg class of Dirichlet series, Duke Math. Journal, 72 No. 3, (1993) 673–693.
H. Jacquet and J.A. Shalika, A non-vanishing theorem for zeta functions of GL n, Inventiones Math., 38 (1976) p. 1–16.
M. Ram Murty, A motivated introduction to the Langlands program, in Advances in Number Theory (eds. F. Gouvea and N. Yui), pp. 37–66, Clarendon Press, Oxford, 1993.
M. Ram Murty, Selberg’s conjectures and Artin L-functions, Bulletin of the Amer. Math. Soc., 31 (1) (1994) p. 1–14.
M. Ram Murty and V. Kumar Murty, Strong multiplicity one for Selberg’s class, C.R. Acad. Sci. Paris, 319 (Series I) (1994) p. 315–320.
M. Ram Murty, Selberg conjectures and Artin L-functions, II, in Current Trends in Mathematics and Physics, A tribute to Harish-Chandra, (edited by S. D. Adhikari), Narosa Publishing House, 1995.
A. Selberg, Old and new conjectures and results about a class of Dirichlet series, Collected Papers, Volume II, pp. 47–63, Springer-Verlag.
M.F. Vignéras, Facteurs gamma et équations fonctionelles, Lecture notes in mathematics, 627 Springer-Verlag, Berlin-New York, 1976.
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Murty, M.R., Murty, V.K. (1997). Selberg’s Conjectures. In: Non-vanishing of L-Functions and Applications. Progress in Mathematics, vol 157. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8956-8_8
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DOI: https://doi.org/10.1007/978-3-0348-8956-8_8
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