Uniform bound for Hecke L-functions
نویسندگان
چکیده
منابع مشابه
An Explicit Formula for Hecke L-functions
In this paper an explicit formula is given for a sequence of numbers. The positivity of this sequence of numbers implies that zeros in the critical strip of the Euler product of Hecke polynomials, which are associated with the space of cusp forms of weight k for Hecke congruence subgroups, lie on the critical line.
متن کامل(Almost) primitivity of Hecke L-functions
Let f be a cusp form of the Hecke space M0(λ, k, ) and let Lf be the normalized L-function associated to f . Recently it has been proved that Lf belongs to an axiomatically defined class of functions S̄. We prove that when λ ≤ 2, Lf is always almost primitive, i.e., that if Lf is written as product of functions in S̄, then one factor, at least, has degree zeros and hence is a Dirichlet polynomial...
متن کاملEffective Nonvanishing of Canonical Hecke L-functions
Motivated by work of Gross, Rohrlich, and more recently Kim, Masri, and Yang, we investigate the nonvanishing of central values of L-functions of “canonical” weight 2k−1 Hecke characters for Q( √ −p), where 3 < p ≡ 3 (mod 4) is prime. Using the work of Rodriguez-Villegas and Zagier, we show that there are nonvanishing central values provided that p ≥ 6.5(k−1) and (−1) ( 2 p ) = 1. Moreover, we ...
متن کاملOn the Bloch-kato Conjecture for Hecke L-functions
Let K be an imaginary quadratic eld and let O K be the ring of integers of K. Let E be an elliptic curve deened over Q with complex multiplication by O. Let be the Grr ossencharacter attached to the curve E over K by the theory of complex multiplication and let be the conjugate character. For k > j > 0, k ?j is a Grr ossencharacter. We will study p? part of the conjecture of Bloch-Kato for the ...
متن کاملExplicit Formulas for Dirichlet and Hecke L-functions
In 1997, the author proved that the Riemann hypothesis holds if and only if λn = ∑ [1−(1−1/ρ)n] > 0 for all positive integers n, where the sum is over all complex zeros of the Riemann zeta function. In 1999, E. Bombieri and J. Lagarias generalized this result and obtained a remarkable general theorem about the location of zeros. They also gave an arithmetic interpretation for the numbers λn. In...
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: Acta Mathematica
سال: 2005
ISSN: 0001-5962
DOI: 10.1007/bf02588051