(Almost) primitivity of Hecke L-functions

نویسندگان

  • G. Molteni
  • J. Steuding
چکیده

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. Moreover, we prove that if λ 6∈ { √ 2, √ 3, 2} then Lf is also primitive, i.e., that if Lf = F1F2 then F1 (or F2) is constant; for λ ∈ { √ 2, √ 3, 2} the factorization of nonprimitive functions is studied and examples of non-primitive functions are given. At last, the subset of functions f for which Lf belongs to the more familiar extended Selberg class S is characterized and for these functions we obtain analogous conclusions about their (almost) primitivity in S.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Number Theory 19 Statistics for low - lying zeros of Hecke L - functions in the level aspect

We would like to provide evidence for the fact that zeros of L-functions seem to behave statistically as eigenvalues of random matrices of large rank throughout the instance of Hecke L-functions. First, we remind you of Iwaniec-Luo-Sarnak’s results on one-level densities for low-lying zeros of Hecke L-functions (see [5]) and Katz-Sarnak’s results on one-level densities for eigenvalues of orthog...

متن کامل

On Hecke L-functions attached to half-integral weight modular forms

We would like to recall that in the case of Hecke eigenforms on Γ1 non-vanishing results for their Hecke L-functions at an arbitrary point s0 in the critical strip (not on the critical line) have been proved in [4] (cf. also [7]), using holomorphic kernel functions. This method was carried over to the case of half-integral weight in [8], for arbitrary level. However, in this approach for given ...

متن کامل

Action of Hecke Operators on Maass Theta Series and Zeta Functions

The introductory part contains definitions and basic properties of harmonic theta series, Siegel modular forms, and Hecke operators. Then the transformation formulas are recalled, related to the action of modular substitutions and regular Hecke operators on general harmonic theta series, including specialization to the case of Maass theta series. The following new results are obtained: construc...

متن کامل

Central Values of Hecke L-functions of Cm Number Fields

0. Introduction. It is well known that the zeta function of CM (complex multiplication) abelian varieties can be given in terms of L-functions of associated Hecke characters. In this paper, we prove a formula expressing the central special value of the L-function of certain Hecke characters in terms of theta functions. The formula easily implies that the central value is nonnegative and yields ...

متن کامل

Hecke L-functions, Eisenstein Series, and the Distribution of Totally Positive Integers

Let K be a number field of degree n. We show that the maximal parabolic Eisenstein series on GL(n), restricted to the non-split torus obtained from K, has a Fourier expansion, and that the Fourier coefficients may be expressed in terms of Hecke L-functions. This is an analogue of the computation of the classical hyperbolic expansion of the GL(2) nonholomorphic Eisenstein series. We also show th...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010