Zobrazeno 1 - 10
of 518
pro vyhledávání: '"SOUNDARARAJAN, K."'
Autor:
Heap, Winston, Soundararajan, K.
This paper describes a method to compute lower bounds for moments of $\zeta$ and $L$-functions. The method is illustrated in the case of moments of $|\zeta(\frac 12+it)|$, where the results are new for small moments $0< k<1$.
Comment: 13 pages
Comment: 13 pages
Externí odkaz:
http://arxiv.org/abs/2007.13154
Autor:
Soundararajan, K.
This is an expository note discussing how the Erdos--Ramanujan proof of Bertrand's postulate may be adapted to show the existence of finite fields.
Comment: 4 pages
Comment: 4 pages
Externí odkaz:
http://arxiv.org/abs/2007.01389
This article is concerned with the Fourier coefficients of cusp forms (not necessarily eigenforms) of half-integer weight lying in the plus space. We give a soft proof that there are infinitely many fundamental discriminants $D$ such that the Fourier
Externí odkaz:
http://arxiv.org/abs/2004.14450
Publikováno v:
Discrete Anal., 2020:6, 19 pp
The Landau-Selberg-Delange method provides an asymptotic formula for the partial sums of a multiplicative function whose average value on primes is a fixed complex number $v$. The shape of this asymptotic implies that $f$ can get very small on averag
Externí odkaz:
http://arxiv.org/abs/1909.13105
Autor:
Brüdern, J., Soundararajan, K.
Motivated by a question of Venkataramana, we consider the greatest common divisor of $\phi(f(n))$ where $f$ is a primitive polynomial with integer coefficients, and $n$ ranges over all natural numbers. Assuming Schinzel's hypothesis, we establish tha
Externí odkaz:
http://arxiv.org/abs/1909.10808
Autor:
Soundararajan, K.
This paper discusses examples of integral factorial ratios of height 2 or more. It classifies (apart from finitely many examples) such factorial ratios with height 2 and norm at most 1/3, and describes a general result which exhibits more than 50 two
Externí odkaz:
http://arxiv.org/abs/1906.06413
Autor:
Soundararajan, K.
This paper describes a new approach to classifying integral factorial ratio, obtaining in particular a direct proof of a result of Bober. These results generalize an observation going back to Chebyshev that $(30n)!n!/((15n)!(10n)!(6n)!)$ is an intege
Externí odkaz:
http://arxiv.org/abs/1901.05133
Autor:
Soundararajan, K.
A classical result of Erdos and Turan states that if a monic polynomial has small size on the unit circle and its constant coefficient is not too small, then its zeros cluster near the unit circle and become equidistributed in angle. Using Fourier an
Externí odkaz:
http://arxiv.org/abs/1802.06506
Publikováno v:
In Complementary Therapies in Clinical Practice November 2022 49
We prove a sharp version of Hal\'asz's theorem on sums $\sum_{n \leq x} f(n)$ of multiplicative functions $f$ with $|f(n)|\le 1$. Our proof avoids the "average of averages" and "integration over $\alpha$" manoeuvres that are present in many of the ex
Externí odkaz:
http://arxiv.org/abs/1706.03755