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On singular primes in function fields
Archiv der Mathematik, 1988Sei F ein separabel erzeugter Funktionenkörper in einer Variablen mit Konstantenkörper K der Charakteristik p. Sei \(F'=K'\cdot F\) eine Konstantenkörpererweiterung. Ein Primdivisor von F heißt K'- regulär, wenn der ganze Abschluß seines lokalen Ringes in F' durch Konstantenkörpererweiterung hervorgeht, andernfalls heißt er K'- singulär.
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Prime Tuples in Function Fields
2016How many prime numbers are there? How are they distributed among other numbers? These are questions that have intrigued mathematicians since ancient times. However, many questions in this area have remained unsolved, and seemingly unsolvable in the forseeable future.
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Reduction of an Algebraic Function Field Modulo a Prime in the Constant Field
The Annals of Mathematics, 1958\(K\) sei ein algebraischer Funktionenkörper mit dem Konstantenkörper \(k\) und \(h\) eine diskrete nicht-archimedische Bewertung von \(k\). Ist \(x\) eine über \(k\) transzendente Größe von \(K\), so werde \(h\) durch \[ \left[\left(\sum_{\nu=0}^r a_\nu x^\nu\right) \left(\sum_{\nu=0}^s b_\nu x^\nu\right)^{-1}\right] = (\max \{h(a_\nu)\}) (\max \{h(b_\
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Covering sumsets of a prime field and class numbers
Research in Mathematical Sciences, 2023Emre Alkan, Alkan Emre
exaly
On Complexity of Search for the Periods of Functions Given by Polynomials over a Prime Field
Journal of Applied and Industrial Mathematics, 2022exaly
The prime ideals of a polynomial ideal under extension of the base field
Annali Di Matematica Pura Ed Applicata, 1975A Seidenberg, Seidenberg A
exaly
Infinite class field towers of number fields of prime power discriminant
Advances in Mathematics, 2020Farshid Hajir
exaly
Design and Implementation of the Primitive Polynomial Search System in the Prime Number Field
Lecture Notes in Electrical Engineering, 2022exaly