An arithmetic formula for certain coefficients of the Euler product of Hecke polynomials

@article{Li2004AnAF,
title={An arithmetic formula for certain coefficients of the Euler product of Hecke polynomials},
author={Xian-jin Li},
journal={Journal of Number Theory},
year={2004},
volume={113},
pages={175-200}
}
• Xian-jin Li
• Published 9 March 2004
• Mathematics
• Journal of Number Theory
6 Citations
Li coefficients for automorphic $L$-functions
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• 2005
In this paper we give an example of a noncongruence subgroup whose three-dimensional space of cusp forms of weight 3 has the following properties. For each of the four residue classes of odd primes
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Congruences for sporadic sequences and modular forms for non-congruence subgroups
In the course of the proof of the irrationality of zeta(2) R. Apery introduced numbers b_n = \sum_{k=0}^n {n \choose k}^2{n+k \choose k}. Stienstra and Beukers showed that for the prime p > 3 Apery
On Li’s coefficients for the Rankin–Selberg L-functions
• Mathematics
• 2010
AbstractWe define a generalized Li coefficient for the L-functions attached to the Rankin–Selberg convolution of two cuspidal unitary automorphic representations π and π′ of $GL_{m}(\mathbb{A}_{F})$

References

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Explicit 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.
Complements to Li's Criterion for the Riemann Hypothesis☆
• Mathematics
• 1999
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
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,
Introduction to the arithmetic theory of automorphic functions
* uschian groups of the first kind * Automorphic forms and functions * Hecke operators and the zeta-functions associated with modular forms * Elliptic curves * Abelian extensions of imaginary
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