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In this paper, building on work of Wiles [Wi] and of Wiles and one of us (R.T.) [TW], we will prove the following two theorems (see Â§2.2). Theorem A. If E/Q is an elliptic curve, then E is modular.â€¦ (More)

- Fred Diamond, Matthias Flach, Li Guo
- 2003

The Tamagawa number conjecture of Bloch and Kato describes the behavior at integers of the L-function associated to a motive over Q. Let f be a newform of weight k â‰¥ 2, level N with coefficients in aâ€¦ (More)

- John Seth Markowitz, C Lindsay Devane, +4 authors Kennerly S. Patrick
- Drug metabolism and disposition: the biologicalâ€¦
- 2000

Ethylphenidate was recently reported as a novel drug metabolite in two overdose fatalities where there was evidence of methylphenidate and ethanol coingestion. This study explores theâ€¦ (More)

- Fred Diamond, Matthias Flach, Li Guo
- 2001

This paper concerns the Tamagawa number conjecture of Bloch and Kato [B-K] for adjoint motives of modular forms of weight k â‰¥ 2. The conjecture relates the value at 0 of the associated L-function toâ€¦ (More)

A generalization of Serreâ€™s Conjecture asserts that if F is a totally real field, then certain characteristic p representations of Galois groups over F arise from Hilbert modular forms. Moreover, itâ€¦ (More)

- Fred Diamond
- Proceedings of the National Academy of Sciencesâ€¦
- 1997

We discuss the relationship among certain generalizations of results of Hida, Ribet, and Wiles on congruences between modular forms. Hida's result accounts for congruences in terms of the value of anâ€¦ (More)

- Fred Diamond
- 1993

The authors would like to give special thanks to N. Boston, K. Buzzard, and B. Conrad for providing so much valuable feedback on earlier versions of this paper. They are also grateful to A. Agboola,â€¦ (More)

- Fred Diamond
- 2009

In 1987 Serre conjectured that any mod ` two-dimensional irreducible odd representation of the absolute Galois group of the rationals came from a modular form in a precise way. We present aâ€¦ (More)

- Fred Diamond, Jerry Shurman, Graduate

A first course in modular forms, It is fair to say that the development of algebraic number theory over the past thirty years has been profoundly influenced by attempts to understand the arithmeticâ€¦ (More)

691 X. Then one can check that f , U n f = Âµ(A âˆ© T âˆ’n A). It follows that f , A N,M (f) = 1 N âˆ’ M Nâˆ’1 n=M Âµ(A âˆ© T âˆ’n A). (g(x) dÂµ) 2 = (f (x) dÂµ) 2 = Âµ(A) 2. Therefore, we deduce that lim Nâˆ’Mâ†’âˆž 1 N âˆ’â€¦ (More)