Distinct zeros of functions in the Selberg class

Kotyada, Srinivas

doi:10.4064/aa103-3-1

Cited by 11 publications

(9 citation statements)

References 4 publications

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“…The probably strongest statement, however, was obtained by Kotyada Srinivas [33], who proved by a different method unconditionally that m L1 (ρ) > m L2 (ρ) for some zero ρ = β + iγ of L 1 • L 2 with deg L 1 deg L 2 and γ from some neighborhood of T for all sufficiently large T . All these papers consider L-functions in the Selberg class; it seems that at least in [33] this restriction can be relaxed.…”

Section: Discussionmentioning

confidence: 99%

Distinguishing L-functions by joint universality

Steuding

2021

Lith Math J

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Section: Discussionmentioning

confidence: 99%

Distinguishing L-functions by joint universality

Steuding

2021

Lith Math J

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“…as w → 0, from (22) and the functional equation for the gamma function, by induction in n (n ∈ N) it is easy to see that…”

Section: Proofmentioning

confidence: 98%

On asymptotic behavior of generalized Li coefficients in the Selberg class

Odžak

Smajlović

2011

Journal of Number Theory

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In this paper we obtain a full asymptotic expansion of the archimedean contribution to the Li coefficients λ F (−n) (n is a positive integer) attached to a function F in the certain class S of functions containing the Selberg class S and (unconditionally) the class of all automorphic L-functions attached to irreducible, unitary cuspidal representations of GL N (Q). Applying the obtained results to automorphic L-functions, we improve the result of J.C. Lagarias concerning the asymptotic behavior of archimedean contribution to the nth Li coefficient attached to the automorphic L-function.We also deduce asymptotic behaviors of λ F (−n), as n → +∞ equivalent to Generalized Riemann Hypothesis (GRH) true and GRH false for F ∈ S .

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“…We may choose σ 0 so that the contour avoids any trivial zero and T = √ n + ǫ n with 0 ≤ ǫ n ≤ 1 so that the horizontal lines do not approach closer than O(log n) to any zero of F (s). Recall from [16] that for −2 < ℜ(s) < 2 there holds…”

Section: Note Thatmentioning

confidence: 99%