منابع مشابه
Zeros of Families of Automorphic L-functions
For many L-functions of arithmetic interest, the values on or close to the edge of the region of absolute convergence are of great importance, as shown for instance by the proof of the Prime Number Theorem (equivalent to non-vanishing of ζ(s) for Re(s) = 1). Other examples are the Dirichlet L-functions (e.g., because of the Dirichlet class-number formula) and the symmetric square L-functions of...
متن کاملZeros of Families of Automorphic L-functions Close to 1
For many L-functions of arithmetic interest, the values on or close to the edge of the region of absolute convergence are of great importance, as shown for instance by the proof of the Prime Number Theorem (equivalent to non-vanishing of ζ(s) for Re(s) = 1). Other examples are the Dirichlet L-functions (e.g. because of the Dirichlet class-number formula) and the symmetric square L-functions of ...
متن کاملTHE ANALYTIC RANK OF J0(q) AND ZEROS OF AUTOMORPHIC L-FUNCTIONS
We study zeros of the L-functions L(f, s) of primitive weight two forms of level q. Our main result is that, on average over forms f of level q prime, the order of the L-functions at the central critical point s = 1 2 is absolutely bounded. On the Birch and Swinnerton-Dyer conjecture, this provides an upper bound for the rank of the Jacobian J0(q) of the modular curve X0(q), which is of the sam...
متن کاملEstimates of Automorphic Functions
We present a new method to estimate trilinear period for automorphic representations of SL2(R). The method is based on the uniqueness principle in representation theory. We show how to separate the exponentially decaying factor in the triple period from the essential automorphic factor which behaves polynomially. We also describe a general method which gives an estimate on the average of the au...
متن کاملOn simple double zeros and badly conditioned zeros of analytic functions of n variables
We give a numerical criterion for a badly conditioned zero of a system of analytic equations to be part of a cluster of two zeros.
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2019
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x19007279