اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدLarge sets of consecutive Maass forms and fluctuations in the Weyl remainder
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تأليف
Holger Then
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We explore an algorithm which systematically finds all discrete eigenvalues of an analytic eigenvalue problem. The algorithm is more simple and elementary as could be expected before. It consists of Hejhals identity, linearisation, and Turing bounds. Using the algorithm, we compute more than one hundredsixty thousand consecutive eigenvalues of the Laplacian on the modular surface, and investigate the asymptotic and statistic properties of the fluctuations in the Weyl remainder. We summarize the findings in two conjectures. One is on the maximum size of the Weyl remainder, and the other is on the distribution of a suitably scaled version of the Weyl remainder.
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