✦ LIBER ✦

Zeros of certain Drinfeld modular functions

✍ Scribed by Matija Kazalicki

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 123 KB
Volume: 128
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2007.02.003

No coin nor oath required. For personal study only.

✦ Synopsis

For every positive integer m, there is a unique Drinfeld modular function, holomorphic on the Drinfeld upper-half plane, j m (z) with the following t-expansion

These functions are analogs of certain modular functions from the classical theory that have many fascinating properties. For example, they are used to prove the famous denominator formula for the Monster Lie algebra. Here we prove that (as in the classical case) the zeros of j m (z) in the fundamental domain F of the Drinfeld upper-half plane Ω for Γ := GL 2 (F q [T ])

1 , are on the unit circle |z| = 1. Moreover, if q is odd, the zeros are transcendental over F q (T ).

📜 SIMILAR VOLUMES

Green's Functions for Drinfeld Modular C

Green's Functions for Drinfeld Modular Curves

✍ Ulrich Tipp 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 220 KB

Let K=F q (T ) be a rational function field and the place given by the degree in T. Let L ÂK be a finite extension with ramification index not bigger than 2. We show in this paper how the local Ne ron Tate height pairing at on Drinfeld modular curves over K of divisors whose points are defined over

The distribution of zeros of certain ent

The distribution of zeros of certain entire functions

✍ J.D De Pree 📂 Article 📅 1965 🏛 Elsevier Science 🌐 English ⚖ 275 KB

On the number of zeros of certain functi

On the number of zeros of certain functions

✍ M Voorhoeve; A.J Van der Poorten; R Tijdeman 📂 Article 📅 1975 🏛 Elsevier Science ⚖ 424 KB

On the Singular Values of the Drinfeld M

On the Singular Values of the Drinfeld Modular Function μ

✍ Daeyeol Jeon; Chang Heon Kim 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 118 KB

In this work we find a uniformizer m of the Drinfeld modular curve X 0 (T) and prove that singular values of m generate ring class fields over an imaginary quadratic field.

Wronskian determinants and the zeros of

Wronskian determinants and the zeros of certain functions

✍ M Voorhoeve; A.J Van Der Poorten 📂 Article 📅 1975 🏛 Elsevier Science ⚖ 370 KB

By relating the problem to the study of the number of zeros of certain wronskian determinants, estimates are found for the number of zeros on the real line of functions of a certain class. This class is instanced by functions of the shape m Z Pt(@ exp Qd-4 k=l where the Pa, QI~ are polynomials and t

Drinfeld Modular Forms of Weight One

✍ Gunther Cornelissen 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 334 KB

Let A=F q [T ] be the polynomial ring over the finite field F q of q elements. D. Goss remarks in [13, (2.1)] that the algebra of (Drinfeld ) modular forms for GL(2, A) is the free ring generated by the two Eisenstein series of weights q&1 and q 2 &1. For a more general congruence subgroup, an abstr