Tag Archives: Naser Sardari

Check the arXiV regularly!

In a previous post, I discussed a new result of Smith which addressed the following question: given a measure \mu on \mathbf{R} supported on some finite union of intervals \Sigma, under what conditions do there exist polynomials of arbitrarily large … Continue reading

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Locally induced representations

Today is a post about work of my student Chengyang Bao. Recall that Lehmer’s conjecture asks whether \tau(p) \ne 0 for all primes p, where \Delta = q \prod_{n=1}^{\infty} (1 – q^n)^{24} = \sum \tau(n) q^n is Ramanujan’s modular form. … Continue reading

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Counting solutions to a_p = λ, Part II

This is a sequel to this post where the problem of counting eigenforms with a_p = \lambda and \lambda \ne 0 was considered. Here we report on recent progress in the case \lambda = 0. It is a somewhat notorious … Continue reading

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Counting solutions to a_p = λ

We know that the eigenvalue of T_2 on \Delta is 24. Are there any other level one cusp forms with the same Hecke eigenvalue? Maeda’s conjecture in its strongest form certainly implies that there does not. But what can one … Continue reading

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