From Weierstrass to Riemann: The Frobenius Pass When Fractal Flows come into Play with Zeta Functions

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Author(s): David, Claire; Lapidus, Michel, L
Source:
Essays in Analytic Number Theory, in Honor of Helmut Maier's 70th Birthday ; https://hal.sorbonne-universite.fr/hal-04614665 ; John Friedlander, Carl Pomerance, and Michael Th. Rassias. Essays in Analytic Number Theory, in Honor of Helmut Maier's 70th Birthday, Springer Nature, Cham, In press
Subject Terms:
effective local and global polyhedral zeta functions; prefractal cohomology; fractal cohomology; transfer operator; Lefschetz operator; Hodge decomposition; functional equation; dual zeta function and Weierstrass Curve; fractal flow; Frobenius operator; Complex Dimensions; MSC Classification: 28A75-28A80-35R02-57Q70 Weierstrass Curve iterated fractal drum (IFD) fractal zeta functions Complex Dimensions of an IFD box-counting (or Minkowski) dimension cohomology infinitesimal intrinsic scale Toda-like system Hodge Diamond Star relation Poincaré duality polyhedral measure polyhedral (or polygonal) neighborhoods effective local and global polyhedral zeta functions prefractal cohomology fractal cohomology transfer operator Lefschetz operator Hodge decomposition functional equation dual zeta function and Weierstrass Curve fractal flow Frobenius operator Complex Dimensions; MSC Classification: 28A75-28A80-35R02-57Q70 Weierstrass Curve; iterated fractal drum (IFD); fractal zeta functions; Complex Dimensions of an IFD; box-counting (or Minkowski) dimension; cohomology infinitesimal; intrinsic scale; Toda-like system; Hodge Diamond Star relation; Poincaré duality; polyhedral measure; polyhedral (or polygonal) neighborhoods; [MATH]Mathematics [math]; [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]; [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT]; [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]; [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV]; [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]
Document Type:
book part
Language:
English

Additional Information
- Contributors:
  Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)); Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité); University of California Riverside (UC Riverside); University of California (UC); John Friedlander; Carl Pomerance; and Michael Th. Rassias
- Publication Information:
  HAL CCSD
  Springer Nature, Cham
- Publication Date:
  2024
- Abstract:
  International audience
- Relation:
  hal-04614665; https://hal.sorbonne-universite.fr/hal-04614665; https://hal.sorbonne-universite.fr/hal-04614665v3/document; https://hal.sorbonne-universite.fr/hal-04614665v3/file/Functional.pdf
- Online Access:
  https://hal.sorbonne-universite.fr/hal-04614665
  https://hal.sorbonne-universite.fr/hal-04614665v3/document
  https://hal.sorbonne-universite.fr/hal-04614665v3/file/Functional.pdf
- Rights:
  info:eu-repo/semantics/OpenAccess
- Accession Number:
  edsbas.18D5BC01

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From Weierstrass to Riemann: The Frobenius Pass When Fractal Flows come into Play with Zeta Functions

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