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Algebraic number theory studies
the arithmetic of algebraic
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arithmetic can be handled mathematically by introducing a congruence relation on the integers that is compatible with the operations on integers: addition, subtraction, and multiplication.For a positive integer n, two numbers a and b are said to be congruent modulo n, if their difference a − b is an integer multiple of n (that is, if there is an integer k such that a − b = kn).
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theory, in particular analytic number
theory, automorphic
forms, L-functions,
quadratic forms. Selected publications: Bounding sup-norms of cusp
forms of large level (with R. Holowinsky), Invent.Math. 179 (2010), 645-681 On the Ramanujan conjecture over number fields (with F. Brumley), Annals of Math. 174 (2011), 581-605 ; Distribution of mass of holomorphic cusp
forms (with …
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Number Theory. Euclid's algorithm and Bezout's theorem.
Arithmetic functions, multiplicative functions. The Mobius function; inversion formula. Dirichlet convolution, Dirichlet inverse. L-Functions and zeta function
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