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Full-Text Articles in Physical Sciences and Mathematics
Congruences For Coefficients Of Modular Functions In Levels 3, 5, And 7 With Poles At 0, Ryan Austin Keck
Congruences For Coefficients Of Modular Functions In Levels 3, 5, And 7 With Poles At 0, Ryan Austin Keck
Theses and Dissertations
We give congruences modulo powers of p in {3, 5, 7} for the Fourier coefficients of certain modular functions in level p with poles only at 0, answering a question posed by Andersen and Jenkins and continuing work done by the Jenkins, the author, and Moss. The congruences involve a modulus that depends on the base p expansion of the modular form's order of vanishing at infinity.
Congruences For Fourier Coefficients Of Modular Functions Of Levels 2 And 4, Eric Brandon Moss
Congruences For Fourier Coefficients Of Modular Functions Of Levels 2 And 4, Eric Brandon Moss
Theses and Dissertations
We give congruences modulo powers of 2 for the Fourier coefficients of certain level 2 modular functions with poles only at 0, answering a question posed by Andersen and Jenkins. The congruences involve a modulus that depends on the binary expansion of the modular form's order of vanishing at infinity. We also demonstrate congruences for Fourier coefficients of some level 4 modular functions.
Weakly Holomorphic Modular Forms In Prime Power Levels Of Genus Zero, David Joshua Thornton
Weakly Holomorphic Modular Forms In Prime Power Levels Of Genus Zero, David Joshua Thornton
Theses and Dissertations
Let N ∈ {8,9,16,25} and let M#0(N) be the space of level N weakly holomorphic modular functions with poles only at the cusp at infinity. We explicitly construct a canonical basis for M#0(N) indexed by the order of the pole at infinity and show that many of the coefficients of the elements of these bases are divisible by high powers of the prime dividing the level N. Additionally, we show that these basis elements satisfy an interesting duality property. We also give an argument that extends level 1 results …