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May 29, 2026Research in the Mathematical SciencesOpen Access

Modular forms for {\, GL\, } (r, FₐT): Hecke operators and growth of expansion coefficients

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Authors

EGErnst-Ulrich Gekeler

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Overview

Randomized trial determines Hecke operator effects on modular form coefficients, suggesting growth insights.

Key Points

  • This research aims to determine the action of Hecke operators on modular forms and explore the growth of expansion coefficients of the discriminant function.
  • Analyzed Hecke operators T_{p,i} on modular forms g_1, ..., g_r, generating the ring of modular forms for GL(r, F_q[T])
  • Characterized eigenforms with respect to prime ideal generators
  • Described the convergence of product and t-expansions of Δ on the fundamental domain.
  • The action of Hecke operators on the forms results in distinct eigenvalues, demonstrated by product expansion behaviors of Δ.
  • t-expansion coefficients for Δ grow under certain conditions, confirming the convergence on the fundamental domain.

Cite This Study

Ernst-Ulrich Gekeler (2026) studied this question.

synapsesocial.com/papers/6a192ea9fab5b468c4417d13https://doi.org/10.1007/s40687-026-00622-1
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