Displaying similar documents to “ L -functions.”

Nonvanishing of automorphic L-functions at special points

Zhao Xu (2014)

Acta Arithmetica

Similarity:

At some special points, we establish a nonvanishing result for automorphic L-functions associated to the even Maass cusp forms in short intervals by using the mollification technique.

K-finite Whittaker functions are of finite order one

(2013)

Acta Arithmetica

Similarity:

We prove a finite order one type estimate for the Whittaker function attached to a K-finite section of a principle series representation of a real or complex Chevalley group. Effective computations are made using convexity in ℂⁿ, following the original paper of Jacquet. As an application, we give a simplified proof of the known result of the boundedness in vertical strips of certain automorphic L-functions, using a result of Müller.

Real zeros of holomorphic Hecke cusp forms and sieving short intervals

Kaisa Matomäki (2016)

Journal of the European Mathematical Society

Similarity:

We study so-called real zeros of holomorphic Hecke cusp forms, that is, zeros on three geodesic segments on which the cusp form (or a multiple of it) takes real values. Ghosh and Sarnak, who were the first to study this problem, showed the existence of many such zeros if many short intervals contain numbers whose prime factors all belong to a certain subset of the primes.We prove new results concerning this sieving problem which leads to improved lower bounds for the number of real zeros. ...

Asymptotically almost automorphic solutions of differential equations with piecewise constant argument

Hui-Sheng Ding, Shun-Mei Wan (2017)

Open Mathematics

Similarity:

This paper is concerned with the existence and uniqueness of asymptotically almost automorphic solutions to differential equations with piecewise constant argument. To study that, we first introduce several notions about asymptotically almost automorphic type functions and obtain some properties of such functions. Then, on the basis of a systematic study on the associated difference system, the existence and uniqueness theorem is established. Compared with some earlier results, we do...