Superposition of zeros of automorphic L-functions and functoriality

Gillespie, Timothy L.

doi:10.17077/etd.iyuhnwkf

Cited by 13 publications

(19 citation statements)

References 30 publications

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“…Remark again that the right-hand side of (8) can be ∞; for instance, Λ Q p = Z, e.g., see (4), (6a) and (6b). By (8), one obtains the following proposition. Proposition 1.…”

Section: Preview and Motivationmentioning

confidence: 93%

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Asymptotic Semicircular Laws Induced by p-Adic Number Fields ℚ p and C*-Algebras over Primes p

Cho

2019

Symmetry

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In this paper, we study asymptotic semicircular laws induced both by arbitrarily fixed C * -probability spaces, and p-adic number fields {Q p } p∈P , as p → ∞ in the set P of all primes.In this paper, we study asymptotic-semicircular laws over "both" primes and unital C * -probability spaces. Since we generalize the asymptotic semicircularity of [25] up to C * -algebra-tensor, the patterns and results of this paper would be similar to those of [25], but generalize-or-universalize them. OverviewIn Section 2, fundamental concepts and backgrounds are introduced. In Sections 3-6, suitable free-probabilistic models are considered, where they contain p-adic number-theoretic information, for our purposes.In Section 7, we establish-and-study C * -probability spaces containing both analytic data from Q p , and free-probabilistic information of fixed unital C * -probability spaces. Then, our free-probabilistic structure LS A , a free product Banach * -probability space, is constructed, and the free probability on LS A is investigated in Section 8.

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“…Remark again that the right-hand side of (8) can be ∞; for instance, Λ Q p = Z, e.g., see (4), (6a) and (6b). By (8), one obtains the following proposition. Proposition 1.…”

Section: Preview and Motivationmentioning

confidence: 93%

“…For number theory and free probability theory, see [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], respectively. In [23], weighted-semicircular elements, and semicircular elements induced by p-adic number fields Q p are considered by the author and Jorgensen, for each p ∈ P, statistically.…”

Section: Preview and Motivationmentioning

confidence: 99%

Asymptotic Semicircular Laws Induced by p-Adic Number Fields ℚ p and C*-Algebras over Primes p

Cho

2019

Symmetry

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“…For some general background on combinatorics of free probability, and facts we use here, the reader is referred to [33,35,39,41]. Analogously, we refer to [7][8][9]17,20,22,23,29,32,36,43] for number theory, and in particular fundamentals on L-functions. The Refs.…”

Section: Free Probabilitymentioning

confidence: 99%

Asymptotic free probability for arithmetic functions and factorization of Dirichlet series

2015

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In this paper, we study a free-probabilistic model on the algebra of arithmetic functions by considering their asymptotic behavior. As an application, we concentrate on arithmetic functions arising from certain representations attached to the general linear group G L n . We then study conditions under which a Dirichlet series may be factored into a product of automorphic L-functions using asymptotic freeness.

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“…Mainly, the prime fields Q p and the adele ring A Q are playing key roles in modern number theory, connected with analytic number theory and algebraic geometry (e.g., [6,9,10] and [15]). Recently, the author and Gillespie have shown that they are also closely related to operator algebraic structures via free probability (e.g., see [1] through [6]).…”

Section: Introductionmentioning

confidence: 99%