caa a22 4500 475738543 CHVBK 20180406123453.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1007/s002220000086 doi (NATIONALLICENCE)springer-10.1007/s002220000086 Mollification of the fourth moment of automorphic L-functions and arithmetic applications [Elektronische Daten] [E. Kowalski, P. Michel, J. VanderKam] Abstract. : We compute the asymptotics of twisted fourth power moments of modular L-functions of large prime level near the critical line. This allows us to prove some new non-vanishing results on the central values of automorphic L-functions, in particular those obtained by base change from GL 2(Q) to GL 2(K) for K a cyclic field of low degree. Springer-Verlag Berlin Heidelberg, 2000 Kowalski E. Department of Mathematics, Fine Hall, Princeton University, Princeton, NJ 08544-1000, USA (e-mail: ekowalsk@math.princeton.edu), US aut Michel P. Institut Universitaire de France et Université Montpellier II CC 051, 34095 Montpellier Cedex 05, France (e-mail: michel@darboux.math.univ-montp2.fr), FR aut VanderKam J. Center for Communications Research, Thanet Road, Princeton, NJ 08540, USA¶(e-mail: vanderkm@idaccr.org), US aut https://doi.org/10.1007/s002220000086 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s002220000086 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kowalski E. Department of Mathematics, Fine Hall, Princeton University, Princeton, NJ 08544-1000, USA (e-mail: ekowalsk@math.princeton.edu), US aut NATIONALLICENCE 700 1- Michel P. Institut Universitaire de France et Université Montpellier II CC 051, 34095 Montpellier Cedex 05, France (e-mail: michel@darboux.math.univ-montp2.fr), FR aut NATIONALLICENCE 700 1- VanderKam J. Center for Communications Research, Thanet Road, Princeton, NJ 08540, USA¶(e-mail: vanderkm@idaccr.org), US aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer