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Endomorphism algebras of motives attached to elliptic modular forms

Alexander F. Brown, Eknath P. Ghate (2003)

Annales de l’institut Fourier

We study the endomorphism algebra of the motive attached to a non-CM elliptic modular cusp form. We prove that this algebra has a sub-algebra isomorphic to a certain crossed product algebra X . The Tate conjecture predicts that X is the full endomorphism algebra of the motive. We also investigate the Brauer class of X . For example we show that if the nebentypus is real and p is a prime that does not divide the level, then the local behaviour of X at a place lying above p is essentially determined...

Equality of Dedekind sums modulo 8ℤ

Emmanuel Tsukerman (2015)

Acta Arithmetica

Using a generalization due to Lerch [Bull. Int. Acad. François Joseph 3 (1896)] of a classical lemma of Zolotarev, employed in Zolotarev's proof of the law of quadratic reciprocity, we determine necessary and sufficient conditions for the difference of two Dedekind sums to be in 8ℤ. These yield new necessary conditions for equality of two Dedekind sums. In addition, we resolve a conjecture of Girstmair [arXiv:1501.00655].

Equations of hyperelliptic modular curves

Josep Gonzalez Rovira (1991)

Annales de l'institut Fourier

We compute, in a unified way, the equations of all hyperelliptic modular curves. The main tool is provided by a class of modular functions introduced by Newman in 1957. The method uses the action of the hyperelliptic involution on the cusps.

Equidistribution of cusp forms on PSL 2 ( 𝐙 ) PSL 2 ( 𝐑 )

Dmitri Jakobson (1997)

Annales de l'institut Fourier

We prove a microlocal version of the equidistribution theorem for Wigner distributions associated to cusp forms on PSL 2 ( Z ) PSL 2 ( R ) . This generalizes a recent result of W. Luo and P. Sarnak who prove equidistribution on PSL 2 ( Z ) H .

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