Displaying similar documents to “Congruences between modular forms and lowering the level mod n

Computing the number of certain Galois representations mod p

Tommaso Giorgio Centeleghe (2011)

Journal de Théorie des Nombres de Bordeaux

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Using the link between Galois representations and modular forms established by Serre’s Conjecture, we compute, for every prime p 2593 , a lower bound for the number of isomorphism classes of Galois representation of Q on a two–dimensional vector space over F ¯ p which are irreducible, odd, and unramified outside p .

Congruences for Siegel modular forms

Dohoon Choi, YoungJu Choie, Olav K. Richter (2011)

Annales de l’institut Fourier

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We employ recent results on Jacobi forms to investigate congruences and filtrations of Siegel modular forms of degree 2 . In particular, we determine when an analog of Atkin’s U ( p ) -operator applied to a Siegel modular form of degree 2 is nonzero modulo a prime p . Furthermore, we discuss explicit examples to illustrate our results.

Class invariants and cyclotomic unit groups from special values of modular units

Amanda Folsom (2008)

Journal de Théorie des Nombres de Bordeaux

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In this article we obtain class invariants and cyclotomic unit groups by considering specializations of modular units. We construct these modular units from functional solutions to higher order q -recurrence equations given by Selberg in his work generalizing the Rogers-Ramanujan identities. As a corollary, we provide a new proof of a result of Zagier and Gupta, originally considered by Gauss, regarding the Gauss periods. These results comprise part of the author’s 2006 Ph.D. thesis []...

Non-abelian congruences between L -values of elliptic curves

Daniel Delbourgo, Tom Ward (2008)

Annales de l’institut Fourier

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Let E be a semistable elliptic curve over . We prove weak forms of Kato’s K 1 -congruences for the special values L 1 , E / ( μ p n , Δ p n ) . More precisely, we show that they are true modulo p n + 1 , rather than modulo p 2 n . Whilst not quite enough to establish that there is a non-abelian L -function living in K 1 p [ [ Gal ( ( μ p , Δ p ) / ) ] ] , they do provide strong evidence towards the existence of such an analytic object. For example, if n = 1 these verify the numerical congruences found by Tim and Vladimir Dokchitser.

A generalization of level-raising congruences for algebraic modular forms

Claus Mazanti Sorensen (2006)

Annales de l’institut Fourier

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In this paper, we extend the results of Ribet and Taylor on level-raising for algebraic modular forms on the multiplicative group of a definite quaternion algebra over a totally real field F . We do this for automorphic representations of an arbitrary reductive group G over F , which is compact at infinity. In the special case where G is an inner form of GSp ( 4 ) over , we use this to produce congruences between Saito-Kurokawa forms and forms with a generic local component.