# Bounds for Arakelov invariants of modular curves

# Bounds for Arakelov invariants of modular curves

This chapter gives bounds for all quantities on the right-hand side in the inequality in Theorems 9.1.1 and 9.2.5, in the context of the modular curves *X*₁(*5l*) with *l* > 5 prime, using the upper bounds for Green functions from Chapter 10. The final estimates are given in the last section of the chapter.

*Keywords:*
modular forms, bounds, inequality, polynomials, Green functions, modular curves

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