Eigenvalues of Hecke Operators on SL(2,Z).
Ein Beitrag zur Arithmetik der Bernoullischen Zahlen imaginär-quadratischer Zahlkörper.
Ein einfacher Beweis der Transformationsformel für log ... (z).
Eine Bemerkung zu einer Arbeit von C. Meyer "Über imaginär-quadratische Körper mit der Klassenzahl 2".
Eisenstein cocycles for GL2Q and values of L-function in real quadratic fields.
Eisenstein Series and Decomposition Theory over Function Fields.
Eisenstein Series and the Distribution of Dedekind Sums.
Eisenstein series on three-dimensional hyperbolic space and imaginary quadratic number fields.
Endomorphism algebras of motives attached to elliptic modular forms
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 . The Tate conjecture predicts that is the full endomorphism algebra of the motive. We also investigate the Brauer class of . For example we show that if the nebentypus is real and is a prime that does not divide the level, then the local behaviour of at a place lying above is essentially determined...
Engendrement par de séries theta de certains espaces de formes modulaires.
Equations of hyperelliptic modular curves
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
We prove a microlocal version of the equidistribution theorem for Wigner distributions associated to cusp forms on . This generalizes a recent result of W. Luo and P. Sarnak who prove equidistribution on .
Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
The convolution sum, [...] ∑(l,m)∈N02αl+βm=nσ(l)σ(m), where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms are used to achieve these evaluations. Since the modular space of level 22 is contained in that of level 44, we almost completely use the basis elements of the modular space of level 44 to carry out the evaluation of the convolution sums for αβ = 22. We then use these convolution sums to determine formulae for the number of representations of a positive integer by...
Explicit Estimates in the Arithmetic Theory of Cusp Forms and Poincaré Series.
Expressing a number as the sum of two coprime squares.
We use hyperbolic geometry to study the limiting behavior of the average number of ways of expressing a number as the sum of two coprime squares. An alternative viewpoint using analytic number theory is also given.