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Petersson Inner Product and Hecke Operators

Covers the Petersson inner product and Hecke operators in modular forms theory, exploring their definitions and properties.

Primes in Arithmetic Progression

Explores primes in arithmetic progression, focusing on L-functions, characters, and the divergence of the sum of 1 over p for p congruent to a modulo q.

Legendre and Jacobi Symbols: RSA Cryptography

Explores Legendre and Jacobi symbols, quadratic residuosity, element orders, and RSA Cryptography complexities.

The Riemann Hypothesis

Explores the Riemann Hypothesis, prime numbers, Zeta-function, and quantum mechanics.

Prime Numbers: Finding and Testing

Covers the definition of a function to determine if a given number is prime.

Fermat's Little Theorem

Explores Fermat's Little Theorem, its extensions, primality testing algorithms, and the significance of prime numbers in cryptography.

Dirichlet Series: Analytic and Algebraic Properties

Explores the analytic and algebraic properties of Dirichlet series associated with arithmetic functions.

Chinese Remainders & RSA

Explores the Chinese Remainders Theorem, RSA public-key cryptosystem, bijective properties, and key generation for encryption and decryption.

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Primes: Fundamental Theorem and Sieve of Eratosthenes

Explores primes, the Fundamental Theorem of Arithmetic, trial division, the Sieve of Eratosthenes, and Euclid's Theorem.