Number Theory

                                      NUMBER THEORY

• Notes from the classroom(taught by professor Shashikant Mulay)

  1. 1. 1 mod 4 primes are sums of two integer squares

     2. Power Congruence

     3. Quadratic Reciprocity

     4. q-Jacobi Sums

     5. Sum of Mobius function over n

     6. Old notes from MATH UTK Fall 2021

• Some problems with solutions(by Dimitrios Nikolakopoulos(me))

• Notes from Purdue University Fall 2023 (taught by professor Trevor D. Wooley)

• Greek notes(by Dimitrios Nikolakopoulos(me))

  1. 1. Θεωρία Αριθμών(taught by professor Dimitrios Chatzakos) UPatras, Spring 2023

• Books: 

  1. 1. A Classical Introduction to Modern Number Theory, K. Ireland and M. Rosen

     2. Elementary Analytic and Geometric Number Theory, H. Iwaniec and W. Narkiewicz and J. Urbanowicz

     3. Geometric and Analytic Number Theory, E. Hlawka and J. Schoiβengeier and R. Taschner

                                      NUMBER THEORY

• Notes from the classroom(taught by professor Shashikant Mulay)

  1. 1. A Bernoulli number formula

     2. Addition formula for ℘

     3. An infinite product for sin z and formula for ζ(2r)

     4. Analytic functions defined by real integrals

     5. Arc-length integral for ellipse and cubic curves

     6. Dirichlet density

     7. Dirichlet Eta function

     8. Lattice moduli and complex-multiplication

     9. Periodic functions

• Some problems with solutions(by Dimitrios Nikolakopoulos(me))

• Books: 

  1. 1. A Classical Introduction to Modern Number Theory, K. Ireland and M. Rosen

     2. Analytic number theory, Henryk Iwaniec and Emmanuel Kowalski

     3. Multiplicative Number Theory, Harold Davenport

     4. Analytic Number Theory, Keith Conrad

     5. Bernoulli Numbers and Zeta Functions, Tsuneo Arakawa and Tomoyoshi Ibukiyama and Masanobu Kaneko

     6. L-συναρτήσεις χαρακτήρων Dirichlet και Θεωρία Πρώτων αριθμών, Διπλωματική εργασία-Λώλης Μιχαήλ

                                      ALGEBRAIC NUMBER THEORY

• Notes from the classroom(taught by professor Rebecca Bellovin)

• Algebraic Number Theory - Notes(by Dimitrios Nikolakopoulos(me))

• Some problems with solutions(by Dimitrios Nikolakopoulos(me))

• Books: 

  1. 1. Number fields, Marcus, Daniel A

     2. Algebraic Number Theory, Local Fields, Jürgen Neukirch

     3. Algebraic Number Theory,  A. Fröhlich, M. J. Taylor

     4. Algebraic Number Theory (2014, Springer), Chap. 7 (Lattices), Frazer Jarvis

     5. Algebraic Number Theory and Fermat’s Last Theorem, Ian Stewart and David Tall, Chap. 6, 7, 8, 9 (Lattices)

                                      MODULAR FORMS

• Modular Forms - Notes(by Dimitrios Nikolakopoulos(me))

• Books: 

  1. 1. 
        

                                      INTEGER PARTITIONS

• Integer Partitions - Notes(by Dimitrios Nikolakopoulos(me))

• Books: 

  1. 1.