# Exponential sums and differential equations

Hi, I have a general question about the relationship between exponential sums and differential equations. In particular, I have been trying to read Katz' work on the subject (his book and his lecture notes) but I am having trouble understanding the big idea and getting confused with all of the algebraic geometry background. Can someone explain the general picture, or direct me towards more elementary works introducing the subject?

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A motivation of the book of N. Katz is study of the monodromy of hypergeometric differential equations. Good pre-references could be Levelt's 1961 PhD thesis "Hypergeometric functions" and [F. Beukers and G. Heckman, Monodromy for the hypergeometric function $_nF_{n-1}$, Invent. Math. 95 (1989) 325--354; dx.doi.org/10.1007/BF01393900]. –  Wadim Zudilin Oct 10 '10 at 22:25