On modular functions in characteristic $p$
نویسندگان
چکیده
منابع مشابه
Gonality of modular curves in characteristic p
Let k be an algebraically closed field of characteristic p. Let X(p;N) be the curve parameterizing elliptic curves with full level N structure (where p N) and full level p Igusa structure. By modular curve, we mean a quotient of any X(p;N) by any subgroup of ((Z/peZ)× × SL2(Z/NZ)) /{±1}. We prove that in any sequence of distinct modular curves over k, the k-gonality tends to infinity. This exte...
متن کاملA RESULT ON MODULAR FORMS IN CHARACTERISTIC p
d The action of the derivation e = q ~ on the q-expansions of modular forms in characteristic p is one of the fundamental tools in the Serre/Swinnerton-Dyer theory of mod p modular forms. In this note, we extend the basic results about this action, already known for P > 5 and level one, to arbitrary p and arbitrary prime-to-p level. !. Review of modular forms in characteristic p We fix an algeb...
متن کاملP. Bonacini HILBERT FUNCTIONS OF DECREASING TYPE IN POSITIVE CHARACTERISTIC
Let C be an integral curve in Pk , with k an algebraically closed field. In the main result of this paper we prove that the Hilbert function of its general plane section C ∩H is of decreasing type, extending to any characteristic a result proved in the case char k = 0 by Maggioni and Ragusa. Moreover, the proof given in this paper does not depend on the uniform position property. We also prove ...
متن کاملRational functions with given ramification in characteristic p
Using limit linear series and a result controlling degeneration from separable maps to inseparable maps, we give a formula for the number of rational functions (up to automorphism of the target) on the projective line with ramification to order ei at general points Pi, in the case that all ei are less than the characteristic. Unlike the case of characteristic 0, the answer is not given by Schub...
متن کاملA RIEMANN HYPOTHESIS FOR CHARACTERISTIC p L-FUNCTIONS
We propose analogs of the classical Generalized Riemann Hypothesis and the Generalized Simplicity Conjecture for the characteristic p L-series associated to function fields over a finite field. These analogs are based on the use of absolute values. Further we use absolute values to give similar reformulations of the classical conjectures (with, perhaps, finitely many exceptional zeroes). We sho...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1978
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1978-0515538-9