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Number Theory Seminar

Friday, October 7, 2022
2:00pm to 3:00pm
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Linde Hall 387
Variants of Lehmer's Conjecture on Ramanujan's tau-function
Ken Ono, Department of Mathematics, University of Virginia,

In the spirit of Lehmer's unresolved speculation on the non-vanishing of Ramanujan's tau-function, it is natural to ask whether a fixed integer is a value of τ(n) , or is a Fourier coefficient of any given modular form. In joint work with J. Balakrishnan, W. Craig, and W.-L. Tsai, the speaker has obtained the first results for such questions. For example, infinitely many spaces are presented for which the primes l<=37 are not absolute values of coefficients of any newforms with integer coefficients. For Ramanujan's tau-function, we offer several infinite families of integers that are never values.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].