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Nonholomorphic Rama...
Nonholomorphic Ramanujan-type congruences for Hurwitz class numbers
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- Beckwith, O. (författare)
- University of Illinois
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- Westerholt-Raum, Martin, 1985 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg
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- Richter, O. K. (författare)
- University of North Texas
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(creator_code:org_t)
- 2020-08-27
- 2020
- Engelska.
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Ingår i: Proceedings of the National Academy of Sciences of the United States of America. - : Proceedings of the National Academy of Sciences. - 0027-8424 .- 1091-6490. ; 117:36, s. 21953-21961
- Relaterad länk:
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Abstract
Ämnesord
Stäng
- In contrast to all other known Ramanujan-type congruences, we discover that Ramanujan-type congruences for Hurwitz class numbers can be supported on nonholomorphic generating series. We establish a divisibility result for such nonholomorphic congruences of Hurwitz class numbers. The two key tools in our proof are the holomorphic projection of products of theta series with a Hurwitz class number generating series and a theorem by Serre, which allows us to rule out certain congruences.
Ämnesord
- 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 -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
Nyckelord
- Hurwitz class numbers
- Ramanujan-type congruences
- holomorphic
- projection
- Chebotarev density theorem
- mock theta-functions
- modular-forms
- projections
- Science & Technology - Other Topics
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- ref (ämneskategori)
- art (ämneskategori)
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