The scores on this exam ranged from 3 to 50, out of a possible Consequences of the Gross—Zagier formulae: Stability of average L -values, subconvexity, and non-vanishing mod p. I awarded Fs to those students who were signed up for the course but did not take the final exam. Recommended Reading: There are quite a few good linear algebra books in circulation; see the textbook lists for some examples. Contributors to the volume: D. Remark on fundamental groups and effective Diophantine methods for hyperbolic curves. OC 3 Page 13 Mar

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Home page for UC Berkeley course Math (linear algebra), spring semester, Professor Kenneth A. Ribet. email: ribet@ as follows: midterm exams 17% each, homework 20%, final exam 46%.

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RIBET Final Exam December 12, 30– PM The scalar field F will be the field of real numbers unless otherwise.

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OC 12 Page 22 Oct On effective equidistribution of expanding translates of certain orbits in the space of lattices. Pages Contributors to the volume: D. Kim H.

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