For germs of holomorphic functions f:(C^ m+ 1, 0) → (C, 0) f:(C m+ 1, 0)→(C, 0), g:(C^ n+ 1,
0) → (C, 0) g:(C n+ 1, 0)→(C, 0) having an isolated critical point at 0 with value 0, the …

In this paper we have estimated one multi-variable character sum\begin {align*}\sum_ {a=
2}^{p-2}\sum_ {b= 1}^{p-1}\sum_ {c= 2}^{p-2}\sum_ {d= 1}^{p-1}\left (\frac {a^ 2-b …

We prove that the coefficients of a ${\rm GL} _3\times {\rm GL} _2 $ Rankin--Selberg $ L $-
function do not correlate with a wide class of trace functions of small conductor modulo …

We prove that the coefficients of a $\mathrm {GL} _3\times\mathrm {GL} _2 $ Rankin--
Selberg $ L $-function do not correlate with a wide class of trace functions of small conductor …

Given a Galois étale map of varieties π: Y→ X and an ℓ‐adic sheaf or complex on Y, we
study two cohomological operations: the tensor direct image and the convolution direct …

We prove a simple explicit formula for the local Katz–Radon transform of an ℓ-adic
representation of the Galois group of the fraction field of a strictly henselian discrete …

We give explicit formulas for the local multiplicative convolution functors, which express the
local monodromies of the convolution of two i-adic sheaves on the torus Gm over the …