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9 papers · 1 filter
On hyperelliptic modular curves over function fields
Mihran Papikian
We prove that there are only finitely many modular curves of -elliptic sheaves over which are hyperelliptic. In odd characteristic we give a complete classific…
Number of Irreducible Polynomials and Pairs of Relatively Prime Polynomials in Several Variables over Finite Fields
Xiang-dong Hou, Gary L. Mullen
We discuss several enumerative results for irreducible polynomials of a given degree and pairs of relatively prime polynomials of given degrees in several variables over finite fie…
Algebraic Values of Transcendental Functions at Algebraic Points
Jingjing Huang, Diego Marques, Martin Mereb
In this paper, the authors will prove that any subset of $\overline{\QQ}$ can be the exceptional set of some transcendental entire function. Furthermore, we could generalize this t…
Some consequences of Schanuel's Conjecture
Chuangxun Cheng, Brian Dietel, Mathilde Herblot +6
During the Arizona Winter School 2008 (held in Tucson, AZ) we worked on the following problems: a) (Expanding a remark by S. Lang). Define Inductively…
Hecke Operators on Drinfeld Cusp Forms
Wen-Ching Winnie Li, Yotsanan Meemark
In this paper, we study the Drinfeld cusp forms for and using Teitelbaum's interpretation as harmonic cocycles. We obtain explicit eigenvalues of Hecke operators as…
Elliptic curves of large rank and small conductor
Noam D. Elkies, Mark Watkins
For r=6,7,...,11 we find an elliptic curve E/Q of rank at least r and the smallest conductor known, improving on the previous records by factors ranging from 1.0136 (for r=6) to ov…