The generalized prime number theorem for automorphic L-functions

Tang, Hengcai

doi:10.1007/s11401-008-0172-0

Cited by 5 publications

(6 citation statements)

References 17 publications

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“…Note that the author in [19] also considered a weighted length spectrum. His object of research were the automorphic L-functions.…”

Section: Remarksmentioning

confidence: 99%

On Some Higher Order Counting Functions for PSL(2,R)

Gusic

2020

Wseas Transactions on Systems and Control

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This paper is devoted to some counting functions of level one and level three in the case of quotient space generated by some strictly hyperbolic Fuchsian group and the upper half-plane. Each of the functions is represented as a sum of some explicit part plus the error term. The explicit part is indexed over singularities of the corresponding Selberg zeta function. In particular, the obtained error term is not larger than O ( x 3/4) . The method applied in this paper follows traditional approach for achieving the error terms in the case of locally symmetric spaces of real rank one. In order to establish an analogy with the classical case, we consider the counting functions divided by x and x3, respectively.

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“…Note that the author in [19] also considered a weighted length spectrum. His object of research were the automorphic L-functions.…”

Section: Remarksmentioning

confidence: 99%

On Some Higher Order Counting Functions for PSL(2,R)

Gusic

2020

Wseas Transactions on Systems and Control

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“…The other measurement results and the corresponding local single-qubit spin rotations are listed in Table 2. Note that Zhang et al and Tang also proposed some schemes for preparing the cluster state by using parity and controlled-phase gates, [22,23] and Ionicioiu implemented cluster state fusion deterministically with parity measurements. [52] Compared to those schemes, the present one is simpler due to there being no requirement for ancilla.…”

Section: Generation Of Multi-particle Entanglement States 31 Four-ele...mentioning

confidence: 99%

“…[54][55][56] We propose a network for the preparation of a novel four-electron entangled state |D (2) 4 ⟩ based on the CNOT gate in Ref. [23] as shown in Fig. 5, which can be written as…”

Section: Four-electron Symmetric Dicke Statementioning

confidence: 99%

“…It has been widely used in quantum teleportation, [1] quantum cryptographic schemes, [2,3] quantum secret sharing, [4][5][6][7] quantum key distribution, [8][9][10][11] and quantum secure direct communication. [12][13][14][15][16][17][18][19][20][21] Moreover, the multi-particle entangled states, e.g., cluster state, [22][23][24][25][26][27] |χ⟩ state, [28] and symmetric Dicke state, [29] occupy an important position in one-way quantum computation due to their high entanglements. [30] Hyperentanglement is the simultaneous entanglement in more than one degree of freedom, such as polarization-momentum, polarization-spatial, spatial-spin, and so on.…”

Section: Introductionmentioning

confidence: 99%

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Complete hyperentangled state analysis and generation of multi-particle entanglement based on charge detection

Jin

Zhu

et al. 2014

Chinese Phys. B

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“…It is well known that the length spectrum stated above easily follows from the corresponding equation for the function ψ k (x), k ∈ N ∪ {0} (these functions are defined below). Such reasoning can be found in [23], as well as in [2]- [4], [12], [14]- [16], [25], [28], etc.…”

Section: Introductionmentioning

confidence: 99%

On the Error Terms of Chebyshev Functions for SL4

Gusic

2020

Wseas Transactions on Systems and Control

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Our object of research are certain higher order counting functions of Chebyshev type, associated to the compact symmetric space SL4. In particular, we consider the function ψ 1 (x) resp. ψ 3 (x), of order 1 resp. 3. As it is well known, any such function can be represented as a sum of some explicit part, and the corresponding error term. The explicit part is usually indexed over singularities of the attached Selberg zeta functions, while the error term depends on the dimension of the underlying symmetric space. Thus, these functions generalize the classical yes function π (x) counting prime geodesics of appropriate length. More precisely, the Chebyshev functions divided by adequate power of x, represent quite natural approximations for the function π (x). In this research, we are particularly interested in the error terms of ψ 1 (x) /x and ψ 3 (x) /x 3 .

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The generalized prime number theorem for automorphic L-functions

Cited by 5 publications

References 17 publications

On Some Higher Order Counting Functions for PSL(2,R)

On Some Higher Order Counting Functions for PSL(2,R)

Complete hyperentangled state analysis and generation of multi-particle entanglement based on charge detection

On the Error Terms of Chebyshev Functions for SL4

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