• Corpus ID: 17850498

An explicit formula for Hecke $L$-functions

@article{Li2004AnEF,
  title={An explicit formula for Hecke \$L\$-functions},
  author={Xian-jin Li},
  journal={arXiv: Number Theory},
  year={2004}
}
  • Xian-jin Li
  • Published 6 March 2004
  • Mathematics
  • arXiv: Number Theory
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. 
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8 Citations
Highly Influential Citations
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Background Citations
3
Methods Citations
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8 Citations

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Citation Type

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References

SHOWING 1-10 OF 18 REFERENCES
An explicit formula for the Euler product of Hecke polynomials
An explicit formula is given for a sequence of numbers by using the Eichler-Selberg trace formula. A criterion is obtained by using these numbers for the location of nontrivial zeros of Hecke…
Topics in classical automorphic forms
Introduction The classical modular forms Automorphic forms in general The Eisenstein and the Poincare series Kloosterman sums Bounds for the Fourier coefficients of cusp forms Hecke operators…
The Positivity of a Sequence of Numbers and the Riemann Hypothesis
Abstract In this note, we prove that the Riemann hypothesis for the Dedekind zeta function is equivalent to the nonnegativity of a sequence of real numbers.
Complements to Li's Criterion for the Riemann Hypothesis☆
Abstract In a recent paper Xian-Jin Li showed that the Riemann Hypothesis holds if and only ifλn=∑ρ [1−(1−1/ρ)n] hasλn>0 forn=1, 2, 3, … whereρruns over the complex zeros of the Riemann zeta…
Automorphic forms on Adele groups
This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of…
La conjecture de Weil. I
© Publications mathematiques de l’I.H.E.S., 1974, tous droits reserves. L’acces aux archives de la revue « Publications mathematiques de l’I.H.E.S. » (http://www.…
MATH
TLDR
It is still unknown whether there are families of tight knots whose lengths grow faster than linearly with crossing numbers, but the largest power has been reduced to 3/z, and some other physical models of knots as flattened ropes or strips which exhibit similar length versus complexity power laws are surveyed.
Siegel zeros and cusp forms
Répartition asymptotique des valeurs propres de l’opérateur de Hecke _
La répartition asymptotique des valeurs propres des opérateurs de Hecke Tp, pour p premier variable, est un problème intéressant et difficile, sur lequel on ne dispose que de résultats partiels, cf.…
Hecke operators on Γ0(m)
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