scholarly journals Density of type-dependent sets in Krull monoids with analytic structure

2021 ◽  
Author(s):  
Maciej Radziejewski
Keyword(s):  
Semigroup Forum ◽  
Zeta Functions ◽  
Analytic Structure ◽  
Link Type ◽  
Krull Monoids ◽  
Counting Functions ◽  
Quantitative Properties

AbstractWe describe structural and quantitative properties of type-dependent sets in monoids with suitable analytic structure, including simple analytic monoids, introduced by Kaczorowski (Semigroup Forum 94:532–555, 2017. 10.1007/s00233-016-9778-9), and formations, as defined by Geroldinger and Halter-Koch (Non-unique factorizations, Chapman and Hall, Boca Raton, 2006. 10.1201/9781420003208). We propose the notions of rank and degree to measure the size of a type-dependent set in structural terms. We also consider various notions of regularity of type-dependent sets, related to the analytic properties of their zeta functions, and obtain results on the counting functions of these sets.

scholarly journals On the cohomology of certain subspaces of $$\text {Sym}^n(\mathbb {P}^1)$$ and Occam’s razor for Hodge structures

2021 ◽  
Vol 8 (2) ◽  
Author(s):  
Oishee Banerjee
Keyword(s):  
Zeta Functions ◽  
The Other ◽  
Grothendieck Ring ◽  
Hodge Structures ◽  
Symmetric Powers ◽  
Link Type ◽  
Occam’S Razor ◽  
Motivic Zeta Functions ◽  
Occam's Razor

AbstractVakil and Matchett-Wood (Discriminants in the Grothendieck ring of varieties, 2013. arXiv:1208.3166) made several conjectures on the topology of symmetric powers of geometrically irreducible varieties based on their computations on motivic zeta functions. Two of those conjectures are about subspaces of $$\text {Sym}^n(\mathbb {P}^1)$$ Sym n ( P 1 ) . In this note, we disprove one of them and prove a stronger form of the other, thereby obtaining (counter)examples to the principle of Occam’s razor for Hodge structures.

scholarly journals Identities for field extensions generalizing the Ohno–Nakagawa relations

2015 ◽  
Vol 151 (11) ◽  
pp. 2059-2075 ◽  
Author(s):  
Henri Cohen ◽  
Simon Rubinstein-Salzedo ◽  
Frank Thorne
Keyword(s):  
Vector Space ◽  
Functional Equations ◽  
Zeta Functions ◽  
Reflection Principle ◽  
Galois Groups ◽  
Field Extensions ◽  
Prehomogeneous Vector Space ◽  
Counting Functions ◽  
Cubic Fields ◽  
Cubic Forms

In previous work, Ohno conjectured, and Nakagawa proved, relations between the counting functions of certain cubic fields. These relations may be viewed as complements to the Scholz reflection principle, and Ohno and Nakagawa deduced them as consequences of ‘extra functional equations’ involving the Shintani zeta functions associated to the prehomogeneous vector space of binary cubic forms. In the present paper, we generalize their result by proving a similar identity relating certain degree-$\ell$ fields to Galois groups $D_{\ell }$ and $F_{\ell }$, respectively, for any odd prime $\ell$; in particular, we give another proof of the Ohno–Nakagawa relation without appealing to binary cubic forms.

SIG 15 Perspectives Vol. 20, No. 3, September 2015

2015 ◽  
Vol 20 (3) ◽  
Keyword(s):  
Learning Center ◽  
Link Type

Abstract Download the CE Questions PDF from the toolbar, above. Use the questions to guide your Perspectives reading. When you're ready, purchase the activity from the ASHA Store and follow the instructions to take the exam in ASHA's Learning Center. Available until August 13, 2018.

SIG 11 Perspectives Vol. 22, No. 2, July 2012

2012 ◽  
Vol 22 (2) ◽  
Author(s):  
Kathryn Taylor ◽  
Emily White ◽  
Rachael Kaplan ◽  
Colleen M. O'Rourke
Keyword(s):  
Link Type

Sorry, this activity is no longer available for CEUs. Visit the SIG 11 page on the ASHA Store to see available CE activities. Use the CE questions PDF here as study questions to guide your Perspectives reading.

SIG 14 Perspectives Vol. 20, No. 3, December 2013

2013 ◽  
Vol 20 (3) ◽  
Keyword(s):  
Link Type

Sorry, this activity is no longer available for CEUs. Visit the SIG 14 page on the ASHA Store to see available CE activities. Use the CE questions PDF here as study questions to guide your Perspectives reading.

SIG 17 Perspectives Vol. 2, No. 1, May 2012

2012 ◽  
Vol 2 (1) ◽  
pp. 1-5
Author(s):  
Celeste Domsch
Keyword(s):  
Link Type

Sorry, this activity is no longer available for CEUs. Visit the SIG 17 page on the ASHA Store to see available CE activities. Use the CE questions PDF here as study questions to guide your Perspectives reading.

SIG 12 Perspectives Vol. 21, No. 4, December 2012

2012 ◽  
Vol 21 (4) ◽  
pp. 1-6 ◽  
Author(s):  
Cathy Binger ◽  
Jennifer Kent-Walsh
Keyword(s):  
Link Type

Sorry, this activity is no longer available for CEUs. Visit the SIG 12 page on the ASHA Store to see available CE activities. Use the CE questions PDF here as study questions to guide your Perspectives reading.

SIG 7 Perspectives Vol. 20, No. 3, December 2013

2013 ◽  
Vol 20 (3) ◽  
Keyword(s):  
Link Type

Sorry, this activity is no longer available for CEUs. Visit the SIG 7 page on the ASHA Store to see available CE activities. Use the CE questions PDF here as study questions to guide your Perspectives reading.

SIG 12 Perspectives Vol. 22, No. 1, April 2013

2013 ◽  
Vol 22 (1) ◽  
pp. 1-5
Author(s):  
Ellen M. Hickey ◽  
Monica McKenna ◽  
Celeste Woods ◽  
Carmen Archibald
Keyword(s):  
Link Type

Sorry, this activity is no longer available for CEUs. Visit the SIG 12 page on the ASHA Store to see available CE activities. Use the CE questions PDF here as study questions to guide your Perspectives reading.

SIG 10 Perspectives Vol. 18, No. 2, October 2015

2015 ◽  
Vol 18 (2) ◽  
Keyword(s):  
Learning Center ◽  
Link Type

Download the CE Questions PDF from the toolbar, above. Use the questions to guide your Perspectives reading. When you're ready, purchase the activity from the ASHA Store and follow the instructions to take the exam in ASHA's Learning Center. Available until July 30, 2018.

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