Modular forms

Modular and cusp forms, congruence subgroups, cusps, Eisenstein series congruences, Ramanujan–Petersson conjecture, spectral gaps.

• Congruences between Eisenstein series and cusp forms
• Hecke operators
• Modular functions
• Modular group and congruence subgroups
• Ramanujan tau function
• Rankin–Selberg coefficients in arithmetic progressions
• Selberg's eigenvalue conjecture
• Ramanujan–Petersson conjecture
• Taylor–Wiles patching
• Weight-two cusp forms on Γ₀(2)

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