Results 11 to 20 of about 263 (30)
Modular equations of a continued fraction of order six
Open Mathematics, 2019 We study a continued fraction X(τ) of order six by using the modular function theory. We first prove the modularity of X(τ), and then we obtain the modular equation of X(τ) of level n for any positive integer n; this includes the result of Vasuki et al ...
Lee Yoonjin, Park Yoon Kyung
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Capitulation of the 2-ideal classes of type (2, 2, 2) of some quartic cyclic number fields
Journal of Mathematical Cryptology, 2019 Let p≡3(mod4){p\equiv 3\pmod{4}} and l≡5(mod8){l\equiv 5\pmod{8}} be different primes such that pl=1{\frac{p}{l}=1} and 2p=pl4{\frac{2}{p}=\frac{p}{l}_{4}}. Put k=ℚ(l){k=\mathbb{Q}(\sqrt{l})}, and denote by ϵ its fundamental unit. Set K=k(-2pϵl){K=k(
Azizi Abdelmalek +3 more
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Curves, dynamical systems and weighted point counting [PDF]
, 2012 Suppose X is a (smooth projective irreducible algebraic) curve over a finite field k. Counting the number of points on X over all finite field extensions of k will not determine the curve uniquely. Actually, a famous theorem of Tate implies that two such
Cornelissen, Gunther
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On a problem of Hasse and Ramachandra
Open Mathematics, 2019 Let K be an imaginary quadratic field, and let 𝔣 be a nontrivial integral ideal of K. Hasse and Ramachandra asked whether the ray class field of K modulo 𝔣 can be generated by a single value of the Weber function. We completely resolve this question when
Koo Ja Kyung +2 more
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An idelic quotient related to Weil reciprocity and the Picard group [PDF]
, 2019 This paper studies the function field of an algebraic curve over an arbitrary perfect field by using the Weil reciprocity law and topologies on the adele ring.
Martín, Francisco José Plaza +3 more
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Ray class invariants over imaginary quadratic fields
, 2011 Let $K$ be an imaginary quadratic field of discriminant less than or equal to -7 and $K_{(N)}$ be its ray class field modulo $N$ for an integer $N$ greater than 1.
Jung, Ho Yun +2 more
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Rigid meromorphic cocycles for orthogonal groups
Forum of Mathematics, SigmaRigid meromorphic cocycles are defined in the setting of orthogonal groups of arbitrary real signature and constructed in some instances via a p-adic analogue of Borcherds’ singular theta lift.
Lennart Gehrmann +2 more
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A counterexample to 'Algebraic function fields with small class number' [PDF]
, 2013 I give a counter example of function field over GF(2) of genus 4 with class number one.
Stirpe, Claudio
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Representing Primes as the Form $x^2+ny^2$ in Some Imaginary Quadratic Fields [PDF]
, 2015 We give criteria of the solvability of the diophantine equation $p=x^2+ny^2$ over some imaginary quadratic fields where $p$ is a prime element. The criteria becomes quite simple in special cases.Comment: 8 pages, This paper has been withdrawn by the ...
Deng, Yingpu, Lv, Chang
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A Study of Kummer's Proof of Fermat's Last Theorem for Regular Primes [PDF]
, 2013 We study Kummer's approach towards proving the Fermat's last Theorem for regular primes. Some basic algebraic prerequisites are also discussed in this report, and also a brief history of the problem is mentioned.
Saikia, Manjil P.
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