scholarly journals Quaternionic Artin representations and nontraditional arithmetic statistics

2019 ◽  
Vol 372 (12) ◽  
pp. 8587-8603
Author(s):  
David E. Rohrlich
Keyword(s):  
Arithmetic Statistics

scholarly journals Arithmetic statistics of modular symbols

2018 ◽  
Vol 212 (3) ◽  
pp. 997-1053 ◽  
Author(s):  
Yiannis N. Petridis ◽  
Morten S. Risager
Keyword(s):  
Modular Symbols ◽  
Arithmetic Statistics

scholarly journals Arithmetic statistics of Galois groups

2019 ◽  
Vol 2 (1) ◽  
pp. 353-374
Author(s):  
David Kohel
Keyword(s):  
Galois Groups ◽  
Arithmetic Statistics

scholarly journals Elliptic Curves with Long Arithmetic Progressions Have Large Rank

2020 ◽  
Author(s):  
Natalia Garcia-Fritz ◽  
Hector Pasten
Keyword(s):  
Elliptic Curves ◽  
Arithmetic Progression ◽  
Nevanlinna Theory ◽  
Uniform Boundedness ◽  
Rational Numbers ◽  
Rational Points ◽  
Arithmetic Progressions ◽  
Large Rank ◽  
Arithmetic Statistics

Abstract For any family of elliptic curves over the rational numbers with fixed $j$-invariant, we prove that the existence of a long sequence of rational points whose $x$-coordinates form a nontrivial arithmetic progression implies that the Mordell–Weil rank is large, and similarly for $y$-coordinates. We give applications related to uniform boundedness of ranks, conjectures by Bremner and Mohanty, and arithmetic statistics on elliptic curves. Our approach involves Nevanlinna theory as well as Rémond’s quantitative extension of results of Faltings.

scholarly journals Étale homological stability and arithmetic statistics

2018 ◽  
Vol 69 (3) ◽  
pp. 951-974
Author(s):  
Benson Farb ◽  
Jesse Wolfson
Keyword(s):  
Homological Stability ◽  
Arithmetic Statistics
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