scholarly journals On the harmonic volume of Fermat curves

2020 ◽  
pp. 1
Author(s):  
Payman Eskandari ◽  
Vijaya Kumar Murty
Keyword(s):  
Fermat Curves

On the Frobenius matrices of fermat curves

1990 ◽  
pp. 173-193 ◽  
Author(s):  
Robert F. Coleman
Keyword(s):  
Fermat Curves

Factorial Fermat curves over the rational numbers

2016 ◽  
Vol 142 (2) ◽  
pp. 285-300
Author(s):  
Peter Malcolmson ◽  
Frank Okoh ◽  
Vasuvedan Srinivas
Keyword(s):  
Rational Numbers ◽  
Fermat Curves

scholarly journals Periods of generalized Fermat curves

2021 ◽  
Vol 225 (1) ◽  
pp. 106465
Author(s):  
Yerko Torres-Nova
Keyword(s):  
Fermat Curves

scholarly journals A characterization of maximal and minimal Fermat curves

2010 ◽  
Vol 16 (1) ◽  
pp. 1-3 ◽  
Author(s):  
Saeed Tafazolian
Keyword(s):  
Fermat Curves

scholarly journals Frobenius Distribution for Quotients of Fermat Curves of Prime Exponent

2016 ◽  
Vol 68 (2) ◽  
pp. 361-394
Author(s):  
Francesc Fité ◽  
Josep González ◽  
Joan-Carles Lario
Keyword(s):  
Abelian Variety ◽  
Complex Multiplication ◽  
Cyclotomic Field ◽  
Explicit Method ◽  
Fermat Curve ◽  
Tate Conjecture ◽  
Tate Group ◽  
Fermat Curves ◽  
Prime Exponent ◽  
Simple Abelian Variety

AbstractLet denote the Fermat curve over ℚ of prime exponent ℓ. The Jacobian Jac() of splits over ℚ as the product of Jacobians Jac(k), 1 ≤ k ≤ ℓ −2, where k are curves obtained as quotients of by certain subgroups of automorphisms of . It is well known that Jac(k) is the power of an absolutely simple abelian variety Bk with complex multiplication. We call degenerate those pairs (ℓ, k) for which Bk has degenerate CM type. For a non-degenerate pair (ℓ, k), we compute the Sato–Tate group of Jac(Ck), prove the generalized Sato–Tate Conjecture for it, and give an explicit method to compute the moments and measures of the involved distributions. Regardless of whether (ℓ, k) is degenerate, we also obtain Frobenius equidistribution results for primes of certain residue degrees in the ℓ-th cyclotomic field. Key to our results is a detailed study of the rank of certain generalized Demjanenko matrices.

Gamma function identities and elliptic differentials on Fermat curves

1978 ◽  
Vol 45 (1) ◽  
pp. 87-99 ◽  
Author(s):  
Neal Koblitz
Keyword(s):  
Gamma Function ◽  
Fermat Curves

Points at infinity on the Fermat curves

1977 ◽  
Vol 39 (2) ◽  
pp. 95-127 ◽  
Author(s):  
David E. Rohrlich
Keyword(s):  
Fermat Curves

Rational points on Fermat curves over finite fields

2017 ◽  
Vol 16 (03) ◽  
pp. 1750046
Author(s):  
Wei Cao ◽  
Shanmeng Han ◽  
Ruyun Wang
Keyword(s):  
Finite Fields ◽  
Rational Point ◽  
Rational Points ◽  
Fermat Curve ◽  
Fermat Curves ◽  
Curves Over Finite Fields

Let [Formula: see text] be the [Formula: see text]-rational point on the Fermat curve [Formula: see text] with [Formula: see text]. It has recently been proved that if [Formula: see text] then each [Formula: see text] is a cube in [Formula: see text]. It is natural to wonder whether there is a generalization to [Formula: see text]. In this paper, we show that the result cannot be extended to [Formula: see text] in general and conjecture that each [Formula: see text] is a cube in [Formula: see text] if and only if [Formula: see text].

The spectrum of fermat curves

1991 ◽  
Vol 1 (1) ◽  
pp. 80-146 ◽  
Author(s):  
R. Phillips ◽  
P. Sarnak
Keyword(s):  
Fermat Curves
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