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.
Shimura's mass formula for an orthogonal group over real quadratic fields
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.
Short character sums with Fermat quotients
Short interval results for k-free values of irreducible polynomials
Short intervals almost all containing primes
Short proofs of theorems of Lekkerkerker and Ballieu.
Short remark on Fibonacci-Wieferich primes
This paper has been inspired by the endeavour of a large number of mathematicians to discover a Fibonacci-Wieferich prime. An exhaustive computer search has not been successful up to the present even though there exists a conjecture that there are infinitely many such primes. This conjecture is based on the assumption that the probability that a prime is Fibonacci-Wieferich is equal to . According to our computational results and some theoretical consideratons, another form of probability can...
Short sums of restricted Möbius functions
Shtukas and Jacobi sums.
Sidon basis in polynomial rings over finite fields
Let denote the polynomial ring over , the finite field of elements. Suppose the characteristic of is not or . We prove that there exist infinitely many such that the set contains a Sidon set which is an additive basis of order .
Siegel Cusp Forms as Holomorphic Differential Forms on Certain Compact Varieties.
Siegel measures.
Siegel Modular Forms of Degree Two: Hecke Eigenforms.
Siegel varieties and -adic Siegel modular forms.