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On the Petersson scalar product of arbitrary modular forms
Petersson scalar product arbitrary modular forms Number Theory
2012/4/18
We consider a natural extension of the Petersson scalar product to the entire space of modular forms of integral weight $k\ge 2$ for a finite index subgroup of the modular group. We show that Hecke op...
Abstract: We show that there are sets of integers with asymptotic density arbitrarily close to 1 in which there is no solution to the equation ab=c, with a,b,c in the set. We also consider some natura...
Squares in Polynomial Product Sequences
Squarefull numbers Polynomial Product Sequences Number Theory
2011/8/31
Abstract: Let F(n) be a polynomial of degree at least 2 with integer coefficients. We consider the products N_x=\prod_{1 \le n \le x} F(n) and show that N_x should only rarely be a perfect power. In p...