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An integrality criterion for elliptic modular forms

Andrea Mori (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let f be an elliptic modular form level of N. We present a criterion for the integrality of f at primes not dividing N. The result is in terms of the values at CM points of the forms obtained applying to f the iterates of the Maaß differential operators.

Arithmetic of the modular function j 1 , 4

Chang Heon Kim, Ja Kyung Koo (1998)

Acta Arithmetica

We find a generator j 1 , 4 of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator N ( j 1 , 4 ) which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.

Calcul du nombre de points sur une courbe elliptique dans un corps fini : aspects algorithmiques

François Morain (1995)

Journal de théorie des nombres de Bordeaux

Nous décrivons dans cet article les algorithmes nécessaires à une implantation efficace de la méthode de Schoof pour le calcul du nombre de points sur une courbe elliptique dans un corps fini. Nous tentons d’unifier pour cela les idées d’Atkin et d’Elkies. En particulier, nous décrivons le calcul d’équations pour X 0 ( ) , premier, ainsi que le calcul efficace de facteurs des polynômes de division d’une courbe elliptique.

Certain L-functions at s = 1/2

Shin-ichiro Mizumoto (1999)

Acta Arithmetica

Introduction. The vanishing orders of L-functions at the centers of their functional equations are interesting objects to study as one sees, for example, from the Birch-Swinnerton-Dyer conjecture on the Hasse-Weil L-functions associated with elliptic curves over number fields.    In this paper we study the central zeros of the following types of L-functions:    (i) the derivatives of the Mellin transforms of Hecke eigenforms for SL₂(ℤ),    (ii) the Rankin-Selberg...

Classical and overconvergent modular forms of higher level

Robert F. Coleman (1997)

Journal de théorie des nombres de Bordeaux

We define the notion overconvergent modular forms on Γ 1 ( N p n ) where p is a prime, N and n are positive integers and N is prime to p . We show that an overconvergent eigenform on Γ 1 ( N p n ) of weight k whose U p -eigenvalue has valuation strictly less than k - 1 is classical.

Cohen-Kuznetsov liftings of quasimodular forms

Min Ho Lee (2015)

Acta Arithmetica

Jacobi-like forms for a discrete subgroup Γ of SL(2,ℝ) are formal power series which generalize Jacobi forms, and they correspond to certain sequences of modular forms for Γ. Given a modular form f, a Jacobi-like form can be constructed by using constant multiples of derivatives of f as coefficients, which is known as the Cohen-Kuznetsov lifting of f. We extend Cohen-Kuznetsov liftings to quasimodular forms by determining an explicit formula for a Jacobi-like form associated to a quasimodular form....

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