Siegel Modular Forms, L-Functions, and Satake Parameters
نویسندگان
چکیده
منابع مشابه
Twisting of Siegel Modular Forms with Characters, and L-functions
Linear twistings of Siegel modular forms with Dirichlet characters are considered. It is shown that the twisting operators transform modular forms to modular forms. Commutation of twisting operators and Hecke operators is examined. It is proved that under certain conditions the spinor zeta-function of a twisted modular form can be interpreted as the L-function of the initial modular form with t...
متن کاملSiegel Modular Forms
These are the lecture notes of the lectures on Siegel modular forms at the Nordfjordeid Summer School on Modular Forms and their Applications. We give a survey of Siegel modular forms and explain the joint work with Carel Faber on vector-valued Siegel modular forms of genus 2 and present evidence for a conjecture of Harder on congruences between Siegel modular forms of genus 1 and 2.
متن کاملCodes and Siegel modular forms
It is proved that the ring of Siegel modular forms in any genus is determined by doubly-even self-dual codes and the theta relations. The (higher) weight polynomials of such codes are proved to be the generators of the ring of invariants of a polynomial ring in 2 g variables under a certain speciied nite group. Moreover codes are uniquely determined by their weight polynomials.
متن کاملSiegel Modular Forms and Representations
This paper explicitly describes the procedure of associating an automorphic representation of PGSp(2n, A) with a Siegel modular form of degree n for the full modular group Γn = Sp(2n, Z), generalizing the well-known procedure for n = 1. This will show that the so-called “standard” and “spin” L-functions associated with such forms are obtained as Langlands L-functions. The theory of Euler produc...
متن کاملSIEGEL MODULAR FORMS ( MOD p ) AND ALGEBRAIC MODULAR FORMS
In his letter [Ser96], J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → F̄p, where B is the endomorphism algebra of a supersingular elliptic curve. After giving a detailed exposition of Serre’s result, we prove that the systems of Hecke eigenvalues given by Siegel modular forms (mod p) o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2001
ISSN: 0022-314X
DOI: 10.1006/jnth.2000.2586