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Mosc. Math. J., 2015, Volume 15, Number 1, Pages 89–100 (Mi mmj550)  

A proof of a conjecture by Lötter on the roots of a supersingular polynomial and its application

Takehiro Hasegawa

Faculty of Education, Shiga University, Otsu, Shiga 520-0862, Japan

Abstract: In this paper, we prove a conjecture by E. C. Lötter on the roots of a supersingular polynomial. As its application, we present two optimal towers over finite fields corresponding to the sequences of elliptic modular curves $X_0(3\cdot2^{n+2})$ and $X_0(2\cdot3^{n+2})$.

Key words and phrases: finite fields, recursive towers of function fields, generating function of the franel number.

DOI: https://doi.org/10.17323/1609-4514-2015-15-1-89-100

Full text: http://www.mathjournals.org/.../2015-015-001-005.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 11R58, 11G20, 14G15
Received: February 13, 2014; in revised form September 16, 2014
Language:

Citation: Takehiro Hasegawa, “A proof of a conjecture by Lötter on the roots of a supersingular polynomial and its application”, Mosc. Math. J., 15:1 (2015), 89–100

Citation in format AMSBIB
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\by Takehiro~Hasegawa
\paper A proof of a~conjecture by L\"otter on the roots of a~supersingular polynomial and its application
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 1
\pages 89--100
\mathnet{http://mi.mathnet.ru/mmj550}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-1-89-100}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3427413}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000354886200005}


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