Philippe Michel

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math.NT2025

Generation of Hecke fields by squares of cyclotomic twists of modular $L$ -values

Valentin Blomer, Ashay Burungale, Philippe Michel +1

Let $f$ be a non-CM elliptic newform without a quadratic inner twist, $p$ an odd prime and $I ¨ $ a Dirichlet character of $p$ -power order and sufficiently large $p$ -power conductor.…

math.NT2025

Bessel Periods on $U (2, 1) \times U (1, 1)$ , Relative Trace Formula and Non-Vanishing of Central $L$ -values

Philippe Michel, Dinakar Ramakrishnan, Liyang Yang

In this paper we calculate the asymptotics of the second moment of the Bessel periods associated to certain holomorphic cuspidal representations $(I ¨ , I ¨ ^{'})$ of $U(2,1) \times U(1,1…

math.NT2024

Relative Trace Formula And Simultaneous Nonvanishing for GL_3 x GL_2 and GL_3 x GL_1 L-functions

Philippe Michel, Dinakar Ramakrishnan, Liyang Yang

Fix a Dirichlet character $I ¨ $ and a cuspidal GL $(2)$ eigenform $I ¨ $ with relatively prime conductors. Then we show that there are infinitely many cusp forms $I ¨ $ on GL $(3)$ such t…

Generation of Hecke fields by squares of cyclotomic twists of modular L-values

Bessel Periods on U(2,1)×U(1,1), Relative Trace Formula and Non-Vanishing of Central L-values

Relative Trace Formula And Simultaneous Nonvanishing for GL_3 x GL_2 and GL_3 x GL_1 L-functions

Generation of Hecke fields by squares of cyclotomic twists of modular $L$ -values

Bessel Periods on $U (2, 1) \times U (1, 1)$ , Relative Trace Formula and Non-Vanishing of Central $L$ -values