Selmer groups and Heegner points in anticyclotomic -extensions
Septic theta function identities in Ramanujan's lost notebook
Series and iterations for 1/π
Séries de Dirichlet et fonctions automorphes
Séries d'Eisenstein et transcendance
Séries thêta des formes quadratiques indéfinies
Several-variable -adic families of Siegel-Hilbert cusp eigensystems and their Galois representations
S-extremal strongly modular lattices
S-extremal strongly modular lattices maximize the minimum of the lattice and its shadow simultaneously. They are a direct generalization of the s-extremal unimodular lattices defined in [6]. If the minimum of the lattice is even, then the dimension of an s-extremal lattices can be bounded by the theory of modular forms. This shows that such lattices are also extremal and that there are only finitely many s-extremal strongly modular lattices of even minimum.
Sheaves of bounded p-adic logarithmic differential forms
Shimura correspondence of Maass wave forms of half integral weight
Shimura lifting on weak Maass forms
There is a Shimura lifting which sends cusp forms of a half-integral weight to holomorphic modular forms of an even integral weight. Niwa and Cipra studied this lifting using the theta series attached to an indefinite quadratic form; later, Borcherds and Bruinier extended this lifting to weakly holomorphic modular forms and harmonic weak Maass forms of weight 1/2, respectively. We apply Niwa's theta kernel to weak Maass forms by using a regularized integral. We show that the lifted function satisfies...
Shimura Varieties and Twisted Orbital Integrals.
Shimura varieties with -level via Hecke algebra isomorphisms: the Drinfeld case
We study the local factor at of the semi-simple zeta function of a Shimura variety of Drinfeld type for a level structure given at by the pro-unipotent radical of an Iwahori subgroup. Our method is an adaptation to this case of the Langlands-Kottwitz counting method. We explicitly determine the corresponding test functions in suitable Hecke algebras, and show their centrality by determining their images under the Hecke algebra isomorphisms of Goldstein, Morris, and Roche.
Shimuras Reziprozitätsgesetz für den Körper der arithmetischen elliptischen Funktionen beliebiger Stufe.
Shintani and Shimura lifts of cusp forms on certain arithmetic groups and their applications
For an odd and squarefree level N, Kohnen proved that there is a canonically defined subspace [...] S κ + 1 2 n e w ( N ) ⊂ S κ + 1 2 ( N ) , and S κ + 1 2 n e w ( N ) and S 2 k n e w ( N ) are isomorphic as modules over the Hecke algebra. Later he gave a formula for the product [...] a g ( m ) a g ( n ) ¯ of two arbitrary Fourier coefficients of a Hecke eigenform g of halfintegral weight and of level 4N in terms of certain cycle integrals of the corresponding form f of integral weight. To this...
Shintani function and its application to automorphic L-functions for classical groups. I. The case of orthogonal groups.
Siegel Cusp Forms as Holomorphic Differential Forms on Certain Compact Varieties.
Siegel Modular Forms of Degree Two: Hecke Eigenforms.
Siegel varieties and -adic Siegel modular forms.
Siegel zeros of Eisenstein series