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NON-VANISHING OF MA...
NON-VANISHING OF MAASS FORM L-FUNCTIONS AT THE CENTRAL POINT
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- Balkanova, O. (author)
- Russian Academy of Sciences
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- Huang, B. R. (author)
- Shandong University
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- Södergren, Anders (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, Algebra och geometri,Department of Mathematical Sciences, Algebra and Geometry,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg
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(creator_code:org_t)
- American Mathematical Society (AMS), 2021
- 2021
- English.
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In: Proceedings of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9939 .- 1088-6826. ; 149:2, s. 509-523
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Abstract
Subject headings
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- In this paper, we consider the family {L-j(s)}(j=1)(infinity) of L-functions associated to an orthonormal basis {u(j)}(j=1)(infinity) of even Hecke-Maass forms for the modular group SL(2, Z) with eigenvalues {lambda(j) = kappa(2)(j) + 1/4}(j=1)(infinity). We prove the following effective non-vanishing result: At least 50% of the central values L-j(1/2) with kappa(j) <= T do not vanish as T -> infinity. Furthermore, we establish effective non-vanishing results in short intervals.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Keyword
- Maass cusp forms
- L-functions
- non-vanishing
- mollification
- automorphic l-functions
- central l-values
- mean-square
- rank
- Mathematics
- Maass cusp forms
Publication and Content Type
- ref (subject category)
- art (subject category)
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