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Let A = {a1, . . . , ak} and B = {b1, . . . , bk} be two subsets of an Abelian group G, k ≤ |G|. Snevily conjectured that, when G is of odd order, there is a permutation π ∈ Sk such that the sums ai+bπ(i), 1 ≤ i ≤ k, are pairwise different. Alon showed that the conjecture is true for groups of prime order, even when A is a sequence of k < |G| elements,… (More)

- Samit Dasgupta
- 2006

Elliptic units, which are obtained by evaluating modular units at quadratic imaginary arguments of the Poincaré upper half-plane, allow the analytic construction of abelian extensions of imaginary quadratic fields. The Kronecker limit formula relates the complex absolute values of these units to values of zeta functions, and allowed Stark to prove his rank… (More)

- Samit Dasgupta
- 1999

- Samit Dasgupta
- 2007

Let F be a totally real number field and let p be a finite prime of F , such that p splits completely in the finite abelian extension H of F . Stark has proposed a conjecture stating the existence of a p-unit in H with absolute values at the places above p specified in terms of the values at zero of the partial zeta-functions associated to H/F . Gross… (More)

Let E be an elliptic curve over Q attached to a newform f of weight two on Γ0(N). Let K be a real quadratic field, and let p||N be a prime of multiplicative reduction for E which is inert in K, so that the p-adic completion Kp of K is the quadratic unramified extension of Qp. Subject to the condition that all the primes dividing M := N/p are split in K, the… (More)

- JOËL BELLAÏCHE, Francesc Castellà, Samit Dasgupta, Matthew Emerton, J. BELLAÏCHE
- 2011

We attach p-adic L-functions to critical modular forms and study them. We prove that those L-functions fit in a two-variables p-adic L-function defined locally everywhere on the eigencurve.

- Samit Dasgupta
- 2014

We prove that the p-adic L-series of the tensor square of a p-ordinary modular form factors as the product of the symmetric square p-adic L-series of the form and a Kubota– Leopoldt p-adic L-series. This establishes a generalization of a conjecture of Citro. Greenberg’s exceptional zero conjecture for the adjoint follows as a corollary of our theorem. Our… (More)

1. A review of the classical setting 2. Elliptic units for real quadratic fields 2.1. p-adic measures 2.2. Double integrals 2.3. Splitting a two-cocycle 2.4. The main conjecture 2.5. Modular symbols and Dedekind sums 2.6. Measures and the Bruhat-Tits tree 2.7. Indefinite integrals 2.8. The action of complex conjugation and of Up 3. Special values of zeta… (More)

Let F be a totally real field and χ an abelian totally odd character of F . In 1988, Gross stated a p-adic analogue of Stark’s conjecture that relates the value of the derivative of the p-adic L-function associated to χ and the p-adic logarithm of a p-unit in the extension of F cut out by χ. In this paper we prove Gross’s conjecture when F is a real… (More)

- Massimo Bertolini, FRANCESC CASTELLA, Henri Darmon, Samit Dasgupta, K. N. Prasanna, Victor Rotger
- 2012

This article surveys six different special value formulae for p-adic L-functions, stressing their common features and their eventual arithmetic applications via Kolyvagin’s theory of “Euler systems”, in the spirit of Coates–Wiles and Kato–Perrin-Riou.