For more information about this meeting, contact Robert Vaughan.
| Title: | Statistics for the traces of cyclic p-covers of curves over finite fields |
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| Seminar: | Algebra and Number Theory Seminar |
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| Speaker: | Chantal David, IAS Princeton |
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| Abstract: |
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| We study in this talk the variation of the trace of the Frobenius endomorphism associated to curves C which have a cyclic p-fold cover over F_q as the curves vary in an irreducible component of the moduli space of cyclic p-covers of a fixed genus g. We show that for q fixed and g increasing, the limiting
distribution of the trace of the Frobenius endomorphism is equal to the sum of q+1 independent random variables taking the value 0 with probability (p-1)/(q+p-1) and each of the p-th roots of unity with equal probability q/(p(q+p-1)). This generalises the work of Kurlberg and Rudnick who considered the same limit for hyperelliptic curves (i.e. cyclic 2-fold covers). We also show that when both the genus and q go to infinity, the normalized trace has a standard complex Gaussian distribution. This is joint work with A. Bucur, B. Feigon and M. Lalin. |
Room Reservation Information
| Room Number: | MB106 |
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| Date: | 12 / 10 / 2009 |
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| Time: | 11:15am - 12:05pm |
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