On the transcendence of special values of Goss L-functions attached to\n Drinfeld modules

2021/10/06 by Oğuz Gezmi̇ş, Gezmiş, Oğuz, Changningphaabi Namoijam +1 · 1 citation
Computer Science · Mathematics · #11G09 #11J93 #11M38 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Coding theory and cryptography #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2110.02569

openalex publication_date 2021/10/06 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Let mathbbF_q be the finite field with q elements and consider the\nrational function field K:= mathbbF_q(\θ). For a Drinfeld module \φ\ndefined over K, we study the transcendence of special values of the Goss\nL-function attached to the abelian t-motive M_\φ of \φ. Moreover,\nwhen \φ is a Drinfeld module of rank r\≥ 2 defined over K which has\neverywhere good reduction, we prove that the value of the Goss L-function\nattached to the (r-1)-st exterior power of M_\φ at any positive integer\nis transcendental over K.\n

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