Geodesic
Real zeros of holomorphic Hecke cusp forms
Journal of the European Mathematical Society, Tome 14 (2012) no. 2, pp. 465-487

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DOI

This note is concerned with the zeros of holomorphic Hecke cusp forms of large weight on the modular surface. The zeros of such forms are symmetric about three geodesic segments and we call those zeros that lie on these segments, real. Our main results give estimates for the number of real zeros as the weight goes to infinity.
DOI : 10.4171/jems/308
Classification : 11-XX, 34-XX, 00-XX
Keywords: Zeros, holomorphic Hecke cusp forms, sieves 
Amit Ghosh; Peter Sarnak. Real zeros of holomorphic Hecke cusp forms. Journal of the European Mathematical Society, Tome 14 (2012) no. 2, pp. 465-487. doi: 10.4171/jems/308
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     author = {Amit Ghosh and Peter Sarnak},
     title = {Real zeros of holomorphic {Hecke} cusp forms},
     journal = {Journal of the European Mathematical Society},
     pages = {465--487},
     year = {2012},
     volume = {14},
     number = {2},
     doi = {10.4171/jems/308},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/308/}
}
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