Primes in arithmetic progressions (II), and Gamma functions

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Hadamard Factorisation

Covers the Hadamard factorisation theorem for entire functions of order at most 1.

Dedekind Function: Analytic Continuation and Euler Product Formula

Covers the Dedekind function, Euler product formula, series convergence, and analytic continuation of logarithmic functions.

Chinese Remainders & RSA

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

Functional Equation of Zeta

Covers the functional equation of zeta function and Jensen's formula in complex analysis.

Prime Number Theorem

Covers the proof of Von Mangoldt's formula and the Prime Number Theorem using Zeta functions and pole analysis.

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.

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Prime Gaps and Multiplicative Sieve Inequalities

Covers the Bombieri-Vinogradov theorem and its implications for prime gaps and multiplicative sieve inequalities.

Harmonic Forms and Riemann Surfaces

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Number Theory: More Facts about Primes

Covers the distribution of primes, arithmetic progressions, Mersene primes, and Goldbach's Conjecture.