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Random differential inclusions with convex right hand sides

Krystyna Grytczuk, Emilia Rotkiewicz (1991)

Annales Polonici Mathematici

 Abstract. The main result of the present paper deals with the existence of solutions of random functional-differential inclusions of the form ẋ(t, ω) ∈ G(t, ω, x(·, ω), ẋ(·, ω)) with G taking as its values nonempty compact and convex subsets of n-dimensional Euclidean space R n .

Real zeros of holomorphic Hecke cusp forms

Amit Ghosh, Peter Sarnak (2012)

Journal of the European Mathematical Society

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.

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